metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C67⋊C3, SmallGroup(201,1)
Series: Derived ►Chief ►Lower central ►Upper central
C67 — C67⋊C3 |
Generators and relations for C67⋊C3
G = < a,b | a67=b3=1, bab-1=a29 >
Character table of C67⋊C3
class | 1 | 3A | 3B | 67A | 67B | 67C | 67D | 67E | 67F | 67G | 67H | 67I | 67J | 67K | 67L | 67M | 67N | 67O | 67P | 67Q | 67R | 67S | 67T | 67U | 67V | |
size | 1 | 67 | 67 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
ρ2 | 1 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
ρ3 | 1 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
ρ4 | 3 | 0 | 0 | ζ6726+ζ6724+ζ6717 | ζ6757+ζ6745+ζ6732 | ζ6740+ζ6721+ζ676 | ζ6752+ζ6748+ζ6734 | ζ6764+ζ6747+ζ6723 | ζ6751+ζ6711+ζ675 | ζ6742+ζ6713+ζ6712 | ζ6737+ζ6729+ζ67 | ζ6763+ζ6753+ζ6718 | ζ6761+ζ6746+ζ6727 | ζ6758+ζ677+ζ672 | ζ6735+ζ6722+ζ6710 | ζ6750+ζ6743+ζ6741 | ζ6766+ζ6738+ζ6730 | ζ6733+ζ6719+ζ6715 | ζ6759+ζ6739+ζ6736 | ζ6755+ζ6754+ζ6725 | ζ6749+ζ6714+ζ674 | ζ6744+ζ6720+ζ673 | ζ6765+ζ6760+ζ679 | ζ6731+ζ6728+ζ678 | ζ6762+ζ6756+ζ6716 | complex faithful |
ρ5 | 3 | 0 | 0 | ζ6742+ζ6713+ζ6712 | ζ6762+ζ6756+ζ6716 | ζ6744+ζ6720+ζ673 | ζ6726+ζ6724+ζ6717 | ζ6757+ζ6745+ζ6732 | ζ6759+ζ6739+ζ6736 | ζ6740+ζ6721+ζ676 | ζ6752+ζ6748+ζ6734 | ζ6765+ζ6760+ζ679 | ζ6764+ζ6747+ζ6723 | ζ6737+ζ6729+ζ67 | ζ6751+ζ6711+ζ675 | ζ6755+ζ6754+ζ6725 | ζ6733+ζ6719+ζ6715 | ζ6750+ζ6743+ζ6741 | ζ6763+ζ6753+ζ6718 | ζ6761+ζ6746+ζ6727 | ζ6758+ζ677+ζ672 | ζ6735+ζ6722+ζ6710 | ζ6766+ζ6738+ζ6730 | ζ6749+ζ6714+ζ674 | ζ6731+ζ6728+ζ678 | complex faithful |
ρ6 | 3 | 0 | 0 | ζ6766+ζ6738+ζ6730 | ζ6740+ζ6721+ζ676 | ζ6750+ζ6743+ζ6741 | ζ6765+ζ6760+ζ679 | ζ6742+ζ6713+ζ6712 | ζ6764+ζ6747+ζ6723 | ζ6733+ζ6719+ζ6715 | ζ6763+ζ6753+ζ6718 | ζ6762+ζ6756+ζ6716 | ζ6726+ζ6724+ζ6717 | ζ6759+ζ6739+ζ6736 | ζ6761+ζ6746+ζ6727 | ζ6737+ζ6729+ζ67 | ζ6749+ζ6714+ζ674 | ζ6758+ζ677+ζ672 | ζ6757+ζ6745+ζ6732 | ζ6752+ζ6748+ζ6734 | ζ6751+ζ6711+ζ675 | ζ6755+ζ6754+ζ6725 | ζ6731+ζ6728+ζ678 | ζ6735+ζ6722+ζ6710 | ζ6744+ζ6720+ζ673 | complex faithful |
ρ7 | 3 | 0 | 0 | ζ6764+ζ6747+ζ6723 | ζ6763+ζ6753+ζ6718 | ζ6762+ζ6756+ζ6716 | ζ6761+ζ6746+ζ6727 | ζ6759+ζ6739+ζ6736 | ζ6758+ζ677+ζ672 | ζ6757+ζ6745+ζ6732 | ζ6755+ζ6754+ζ6725 | ζ6752+ζ6748+ζ6734 | ζ6751+ζ6711+ζ675 | ζ6750+ζ6743+ζ6741 | ζ6749+ζ6714+ζ674 | ζ6744+ζ6720+ζ673 | ζ6742+ζ6713+ζ6712 | ζ6740+ζ6721+ζ676 | ζ6737+ζ6729+ζ67 | ζ6735+ζ6722+ζ6710 | ζ6733+ζ6719+ζ6715 | ζ6731+ζ6728+ζ678 | ζ6726+ζ6724+ζ6717 | ζ6766+ζ6738+ζ6730 | ζ6765+ζ6760+ζ679 | complex faithful |
ρ8 | 3 | 0 | 0 | ζ6749+ζ6714+ζ674 | ζ6750+ζ6743+ζ6741 | ζ6737+ζ6729+ζ67 | ζ6731+ζ6728+ζ678 | ζ6733+ζ6719+ζ6715 | ζ6742+ζ6713+ζ6712 | ζ6758+ζ677+ζ672 | ζ6762+ζ6756+ζ6716 | ζ6744+ζ6720+ζ673 | ζ6766+ζ6738+ζ6730 | ζ6757+ζ6745+ζ6732 | ζ6726+ζ6724+ζ6717 | ζ6763+ζ6753+ζ6718 | ζ6751+ζ6711+ζ675 | ζ6759+ζ6739+ζ6736 | ζ6740+ζ6721+ζ676 | ζ6765+ζ6760+ζ679 | ζ6764+ζ6747+ζ6723 | ζ6752+ζ6748+ζ6734 | ζ6735+ζ6722+ζ6710 | ζ6761+ζ6746+ζ6727 | ζ6755+ζ6754+ζ6725 | complex faithful |
ρ9 | 3 | 0 | 0 | ζ6731+ζ6728+ζ678 | ζ6733+ζ6719+ζ6715 | ζ6758+ζ677+ζ672 | ζ6762+ζ6756+ζ6716 | ζ6766+ζ6738+ζ6730 | ζ6726+ζ6724+ζ6717 | ζ6749+ζ6714+ζ674 | ζ6757+ζ6745+ζ6732 | ζ6740+ζ6721+ζ676 | ζ6765+ζ6760+ζ679 | ζ6764+ζ6747+ζ6723 | ζ6752+ζ6748+ζ6734 | ζ6759+ζ6739+ζ6736 | ζ6735+ζ6722+ζ6710 | ζ6751+ζ6711+ζ675 | ζ6742+ζ6713+ζ6712 | ζ6763+ζ6753+ζ6718 | ζ6761+ζ6746+ζ6727 | ζ6737+ζ6729+ζ67 | ζ6744+ζ6720+ζ673 | ζ6755+ζ6754+ζ6725 | ζ6750+ζ6743+ζ6741 | complex faithful |
ρ10 | 3 | 0 | 0 | ζ6755+ζ6754+ζ6725 | ζ6751+ζ6711+ζ675 | ζ6764+ζ6747+ζ6723 | ζ6750+ζ6743+ζ6741 | ζ6735+ζ6722+ζ6710 | ζ6731+ζ6728+ζ678 | ζ6761+ζ6746+ζ6727 | ζ6733+ζ6719+ζ6715 | ζ6758+ζ677+ζ672 | ζ6744+ζ6720+ζ673 | ζ6766+ζ6738+ζ6730 | ζ6762+ζ6756+ζ6716 | ζ6742+ζ6713+ζ6712 | ζ6752+ζ6748+ζ6734 | ζ6726+ζ6724+ζ6717 | ζ6749+ζ6714+ζ674 | ζ6740+ζ6721+ζ676 | ζ6765+ζ6760+ζ679 | ζ6757+ζ6745+ζ6732 | ζ6737+ζ6729+ζ67 | ζ6763+ζ6753+ζ6718 | ζ6759+ζ6739+ζ6736 | complex faithful |
ρ11 | 3 | 0 | 0 | ζ6763+ζ6753+ζ6718 | ζ6726+ζ6724+ζ6717 | ζ6766+ζ6738+ζ6730 | ζ6759+ζ6739+ζ6736 | ζ6752+ζ6748+ζ6734 | ζ6755+ζ6754+ζ6725 | ζ6765+ζ6760+ζ679 | ζ6751+ζ6711+ζ675 | ζ6764+ζ6747+ζ6723 | ζ6737+ζ6729+ζ67 | ζ6735+ζ6722+ζ6710 | ζ6750+ζ6743+ζ6741 | ζ6749+ζ6714+ζ674 | ζ6762+ζ6756+ζ6716 | ζ6731+ζ6728+ζ678 | ζ6761+ζ6746+ζ6727 | ζ6758+ζ677+ζ672 | ζ6744+ζ6720+ζ673 | ζ6733+ζ6719+ζ6715 | ζ6757+ζ6745+ζ6732 | ζ6740+ζ6721+ζ676 | ζ6742+ζ6713+ζ6712 | complex faithful |
ρ12 | 3 | 0 | 0 | ζ6751+ζ6711+ζ675 | ζ6737+ζ6729+ζ67 | ζ6763+ζ6753+ζ6718 | ζ6735+ζ6722+ζ6710 | ζ6758+ζ677+ζ672 | ζ6733+ζ6719+ζ6715 | ζ6759+ζ6739+ζ6736 | ζ6744+ζ6720+ζ673 | ζ6755+ζ6754+ζ6725 | ζ6749+ζ6714+ζ674 | ζ6740+ζ6721+ζ676 | ζ6766+ζ6738+ζ6730 | ζ6762+ζ6756+ζ6716 | ζ6764+ζ6747+ζ6723 | ζ6757+ζ6745+ζ6732 | ζ6750+ζ6743+ζ6741 | ζ6731+ζ6728+ζ678 | ζ6742+ζ6713+ζ6712 | ζ6765+ζ6760+ζ679 | ζ6761+ζ6746+ζ6727 | ζ6726+ζ6724+ζ6717 | ζ6752+ζ6748+ζ6734 | complex faithful |
ρ13 | 3 | 0 | 0 | ζ6735+ζ6722+ζ6710 | ζ6758+ζ677+ζ672 | ζ6759+ζ6739+ζ6736 | ζ6744+ζ6720+ζ673 | ζ6749+ζ6714+ζ674 | ζ6766+ζ6738+ζ6730 | ζ6751+ζ6711+ζ675 | ζ6740+ζ6721+ζ676 | ζ6750+ζ6743+ζ6741 | ζ6731+ζ6728+ζ678 | ζ6742+ζ6713+ζ6712 | ζ6765+ζ6760+ζ679 | ζ6757+ζ6745+ζ6732 | ζ6761+ζ6746+ζ6727 | ζ6764+ζ6747+ζ6723 | ζ6733+ζ6719+ζ6715 | ζ6762+ζ6756+ζ6716 | ζ6726+ζ6724+ζ6717 | ζ6763+ζ6753+ζ6718 | ζ6755+ζ6754+ζ6725 | ζ6752+ζ6748+ζ6734 | ζ6737+ζ6729+ζ67 | complex faithful |
ρ14 | 3 | 0 | 0 | ζ6744+ζ6720+ζ673 | ζ6749+ζ6714+ζ674 | ζ6751+ζ6711+ζ675 | ζ6740+ζ6721+ζ676 | ζ6731+ζ6728+ζ678 | ζ6765+ζ6760+ζ679 | ζ6735+ζ6722+ζ6710 | ζ6742+ζ6713+ζ6712 | ζ6733+ζ6719+ζ6715 | ζ6762+ζ6756+ζ6716 | ζ6726+ζ6724+ζ6717 | ζ6763+ζ6753+ζ6718 | ζ6764+ζ6747+ζ6723 | ζ6755+ζ6754+ζ6725 | ζ6761+ζ6746+ζ6727 | ζ6766+ζ6738+ζ6730 | ζ6757+ζ6745+ζ6732 | ζ6752+ζ6748+ζ6734 | ζ6759+ζ6739+ζ6736 | ζ6750+ζ6743+ζ6741 | ζ6737+ζ6729+ζ67 | ζ6758+ζ677+ζ672 | complex faithful |
ρ15 | 3 | 0 | 0 | ζ6762+ζ6756+ζ6716 | ζ6766+ζ6738+ζ6730 | ζ6749+ζ6714+ζ674 | ζ6757+ζ6745+ζ6732 | ζ6765+ζ6760+ζ679 | ζ6752+ζ6748+ζ6734 | ζ6731+ζ6728+ζ678 | ζ6764+ζ6747+ζ6723 | ζ6742+ζ6713+ζ6712 | ζ6763+ζ6753+ζ6718 | ζ6761+ζ6746+ζ6727 | ζ6737+ζ6729+ζ67 | ζ6751+ζ6711+ζ675 | ζ6744+ζ6720+ζ673 | ζ6735+ζ6722+ζ6710 | ζ6726+ζ6724+ζ6717 | ζ6759+ζ6739+ζ6736 | ζ6755+ζ6754+ζ6725 | ζ6758+ζ677+ζ672 | ζ6740+ζ6721+ζ676 | ζ6750+ζ6743+ζ6741 | ζ6733+ζ6719+ζ6715 | complex faithful |
ρ16 | 3 | 0 | 0 | ζ6733+ζ6719+ζ6715 | ζ6744+ζ6720+ζ673 | ζ6755+ζ6754+ζ6725 | ζ6766+ζ6738+ζ6730 | ζ6740+ζ6721+ζ676 | ζ6757+ζ6745+ζ6732 | ζ6750+ζ6743+ζ6741 | ζ6765+ζ6760+ζ679 | ζ6731+ζ6728+ζ678 | ζ6742+ζ6713+ζ6712 | ζ6763+ζ6753+ζ6718 | ζ6764+ζ6747+ζ6723 | ζ6752+ζ6748+ζ6734 | ζ6758+ζ677+ζ672 | ζ6737+ζ6729+ζ67 | ζ6762+ζ6756+ζ6716 | ζ6726+ζ6724+ζ6717 | ζ6759+ζ6739+ζ6736 | ζ6761+ζ6746+ζ6727 | ζ6749+ζ6714+ζ674 | ζ6751+ζ6711+ζ675 | ζ6735+ζ6722+ζ6710 | complex faithful |
ρ17 | 3 | 0 | 0 | ζ6757+ζ6745+ζ6732 | ζ6765+ζ6760+ζ679 | ζ6731+ζ6728+ζ678 | ζ6764+ζ6747+ζ6723 | ζ6763+ζ6753+ζ6718 | ζ6737+ζ6729+ζ67 | ζ6762+ζ6756+ζ6716 | ζ6761+ζ6746+ζ6727 | ζ6726+ζ6724+ζ6717 | ζ6759+ζ6739+ζ6736 | ζ6755+ζ6754+ζ6725 | ζ6758+ζ677+ζ672 | ζ6735+ζ6722+ζ6710 | ζ6740+ζ6721+ζ676 | ζ6744+ζ6720+ζ673 | ζ6752+ζ6748+ζ6734 | ζ6751+ζ6711+ζ675 | ζ6750+ζ6743+ζ6741 | ζ6749+ζ6714+ζ674 | ζ6742+ζ6713+ζ6712 | ζ6733+ζ6719+ζ6715 | ζ6766+ζ6738+ζ6730 | complex faithful |
ρ18 | 3 | 0 | 0 | ζ6737+ζ6729+ζ67 | ζ6761+ζ6746+ζ6727 | ζ6726+ζ6724+ζ6717 | ζ6758+ζ677+ζ672 | ζ6755+ζ6754+ζ6725 | ζ6744+ζ6720+ζ673 | ζ6752+ζ6748+ζ6734 | ζ6749+ζ6714+ζ674 | ζ6751+ζ6711+ζ675 | ζ6750+ζ6743+ζ6741 | ζ6731+ζ6728+ζ678 | ζ6740+ζ6721+ζ676 | ζ6766+ζ6738+ζ6730 | ζ6763+ζ6753+ζ6718 | ζ6765+ζ6760+ζ679 | ζ6735+ζ6722+ζ6710 | ζ6733+ζ6719+ζ6715 | ζ6762+ζ6756+ζ6716 | ζ6742+ζ6713+ζ6712 | ζ6759+ζ6739+ζ6736 | ζ6757+ζ6745+ζ6732 | ζ6764+ζ6747+ζ6723 | complex faithful |
ρ19 | 3 | 0 | 0 | ζ6758+ζ677+ζ672 | ζ6755+ζ6754+ζ6725 | ζ6752+ζ6748+ζ6734 | ζ6749+ζ6714+ζ674 | ζ6750+ζ6743+ζ6741 | ζ6740+ζ6721+ζ676 | ζ6737+ζ6729+ζ67 | ζ6731+ζ6728+ζ678 | ζ6735+ζ6722+ζ6710 | ζ6733+ζ6719+ζ6715 | ζ6762+ζ6756+ζ6716 | ζ6742+ζ6713+ζ6712 | ζ6765+ζ6760+ζ679 | ζ6759+ζ6739+ζ6736 | ζ6763+ζ6753+ζ6718 | ζ6744+ζ6720+ζ673 | ζ6766+ζ6738+ζ6730 | ζ6757+ζ6745+ζ6732 | ζ6726+ζ6724+ζ6717 | ζ6751+ζ6711+ζ675 | ζ6764+ζ6747+ζ6723 | ζ6761+ζ6746+ζ6727 | complex faithful |
ρ20 | 3 | 0 | 0 | ζ6740+ζ6721+ζ676 | ζ6731+ζ6728+ζ678 | ζ6735+ζ6722+ζ6710 | ζ6742+ζ6713+ζ6712 | ζ6762+ζ6756+ζ6716 | ζ6763+ζ6753+ζ6718 | ζ6744+ζ6720+ζ673 | ζ6726+ζ6724+ζ6717 | ζ6766+ζ6738+ζ6730 | ζ6757+ζ6745+ζ6732 | ζ6752+ζ6748+ζ6734 | ζ6759+ζ6739+ζ6736 | ζ6761+ζ6746+ζ6727 | ζ6750+ζ6743+ζ6741 | ζ6755+ζ6754+ζ6725 | ζ6765+ζ6760+ζ679 | ζ6764+ζ6747+ζ6723 | ζ6737+ζ6729+ζ67 | ζ6751+ζ6711+ζ675 | ζ6733+ζ6719+ζ6715 | ζ6758+ζ677+ζ672 | ζ6749+ζ6714+ζ674 | complex faithful |
ρ21 | 3 | 0 | 0 | ζ6761+ζ6746+ζ6727 | ζ6759+ζ6739+ζ6736 | ζ6757+ζ6745+ζ6732 | ζ6755+ζ6754+ζ6725 | ζ6751+ζ6711+ζ675 | ζ6749+ζ6714+ζ674 | ζ6764+ζ6747+ζ6723 | ζ6750+ζ6743+ζ6741 | ζ6737+ζ6729+ζ67 | ζ6735+ζ6722+ζ6710 | ζ6733+ζ6719+ζ6715 | ζ6731+ζ6728+ζ678 | ζ6740+ζ6721+ζ676 | ζ6726+ζ6724+ζ6717 | ζ6742+ζ6713+ζ6712 | ζ6758+ζ677+ζ672 | ζ6744+ζ6720+ζ673 | ζ6766+ζ6738+ζ6730 | ζ6762+ζ6756+ζ6716 | ζ6752+ζ6748+ζ6734 | ζ6765+ζ6760+ζ679 | ζ6763+ζ6753+ζ6718 | complex faithful |
ρ22 | 3 | 0 | 0 | ζ6759+ζ6739+ζ6736 | ζ6752+ζ6748+ζ6734 | ζ6765+ζ6760+ζ679 | ζ6751+ζ6711+ζ675 | ζ6737+ζ6729+ζ67 | ζ6750+ζ6743+ζ6741 | ζ6763+ζ6753+ζ6718 | ζ6735+ζ6722+ζ6710 | ζ6761+ζ6746+ζ6727 | ζ6758+ζ677+ζ672 | ζ6744+ζ6720+ζ673 | ζ6733+ζ6719+ζ6715 | ζ6731+ζ6728+ζ678 | ζ6757+ζ6745+ζ6732 | ζ6762+ζ6756+ζ6716 | ζ6755+ζ6754+ζ6725 | ζ6749+ζ6714+ζ674 | ζ6740+ζ6721+ζ676 | ζ6766+ζ6738+ζ6730 | ζ6764+ζ6747+ζ6723 | ζ6742+ζ6713+ζ6712 | ζ6726+ζ6724+ζ6717 | complex faithful |
ρ23 | 3 | 0 | 0 | ζ6765+ζ6760+ζ679 | ζ6742+ζ6713+ζ6712 | ζ6733+ζ6719+ζ6715 | ζ6763+ζ6753+ζ6718 | ζ6726+ζ6724+ζ6717 | ζ6761+ζ6746+ζ6727 | ζ6766+ζ6738+ζ6730 | ζ6759+ζ6739+ζ6736 | ζ6757+ζ6745+ζ6732 | ζ6752+ζ6748+ζ6734 | ζ6751+ζ6711+ζ675 | ζ6755+ζ6754+ζ6725 | ζ6758+ζ677+ζ672 | ζ6731+ζ6728+ζ678 | ζ6749+ζ6714+ζ674 | ζ6764+ζ6747+ζ6723 | ζ6737+ζ6729+ζ67 | ζ6735+ζ6722+ζ6710 | ζ6750+ζ6743+ζ6741 | ζ6762+ζ6756+ζ6716 | ζ6744+ζ6720+ζ673 | ζ6740+ζ6721+ζ676 | complex faithful |
ρ24 | 3 | 0 | 0 | ζ6750+ζ6743+ζ6741 | ζ6735+ζ6722+ζ6710 | ζ6761+ζ6746+ζ6727 | ζ6733+ζ6719+ζ6715 | ζ6744+ζ6720+ζ673 | ζ6762+ζ6756+ζ6716 | ζ6755+ζ6754+ζ6725 | ζ6766+ζ6738+ζ6730 | ζ6749+ζ6714+ζ674 | ζ6740+ζ6721+ζ676 | ζ6765+ζ6760+ζ679 | ζ6757+ζ6745+ζ6732 | ζ6726+ζ6724+ζ6717 | ζ6737+ζ6729+ζ67 | ζ6752+ζ6748+ζ6734 | ζ6731+ζ6728+ζ678 | ζ6742+ζ6713+ζ6712 | ζ6763+ζ6753+ζ6718 | ζ6764+ζ6747+ζ6723 | ζ6758+ζ677+ζ672 | ζ6759+ζ6739+ζ6736 | ζ6751+ζ6711+ζ675 | complex faithful |
ρ25 | 3 | 0 | 0 | ζ6752+ζ6748+ζ6734 | ζ6764+ζ6747+ζ6723 | ζ6742+ζ6713+ζ6712 | ζ6737+ζ6729+ζ67 | ζ6761+ζ6746+ζ6727 | ζ6735+ζ6722+ζ6710 | ζ6726+ζ6724+ζ6717 | ζ6758+ζ677+ζ672 | ζ6759+ζ6739+ζ6736 | ζ6755+ζ6754+ζ6725 | ζ6749+ζ6714+ζ674 | ζ6744+ζ6720+ζ673 | ζ6733+ζ6719+ζ6715 | ζ6765+ζ6760+ζ679 | ζ6766+ζ6738+ζ6730 | ζ6751+ζ6711+ζ675 | ζ6750+ζ6743+ζ6741 | ζ6731+ζ6728+ζ678 | ζ6740+ζ6721+ζ676 | ζ6763+ζ6753+ζ6718 | ζ6762+ζ6756+ζ6716 | ζ6757+ζ6745+ζ6732 | complex faithful |
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67)
(2 38 30)(3 8 59)(4 45 21)(5 15 50)(6 52 12)(7 22 41)(9 29 32)(10 66 61)(11 36 23)(13 43 14)(16 20 34)(17 57 63)(18 27 25)(19 64 54)(24 48 65)(26 55 56)(28 62 47)(31 39 67)(33 46 58)(35 53 49)(37 60 40)(42 44 51)
G:=sub<Sym(67)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67), (2,38,30)(3,8,59)(4,45,21)(5,15,50)(6,52,12)(7,22,41)(9,29,32)(10,66,61)(11,36,23)(13,43,14)(16,20,34)(17,57,63)(18,27,25)(19,64,54)(24,48,65)(26,55,56)(28,62,47)(31,39,67)(33,46,58)(35,53,49)(37,60,40)(42,44,51)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67), (2,38,30)(3,8,59)(4,45,21)(5,15,50)(6,52,12)(7,22,41)(9,29,32)(10,66,61)(11,36,23)(13,43,14)(16,20,34)(17,57,63)(18,27,25)(19,64,54)(24,48,65)(26,55,56)(28,62,47)(31,39,67)(33,46,58)(35,53,49)(37,60,40)(42,44,51) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67)], [(2,38,30),(3,8,59),(4,45,21),(5,15,50),(6,52,12),(7,22,41),(9,29,32),(10,66,61),(11,36,23),(13,43,14),(16,20,34),(17,57,63),(18,27,25),(19,64,54),(24,48,65),(26,55,56),(28,62,47),(31,39,67),(33,46,58),(35,53,49),(37,60,40),(42,44,51)]])
C67⋊C3 is a maximal subgroup of
C67⋊C6
Matrix representation of C67⋊C3 ►in GL3(𝔽1609) generated by
0 | 1 | 0 |
0 | 0 | 1 |
1 | 16 | 447 |
1 | 0 | 0 |
1462 | 597 | 1256 |
629 | 1180 | 1011 |
G:=sub<GL(3,GF(1609))| [0,0,1,1,0,16,0,1,447],[1,1462,629,0,597,1180,0,1256,1011] >;
C67⋊C3 in GAP, Magma, Sage, TeX
C_{67}\rtimes C_3
% in TeX
G:=Group("C67:C3");
// GroupNames label
G:=SmallGroup(201,1);
// by ID
G=gap.SmallGroup(201,1);
# by ID
G:=PCGroup([2,-3,-67,445]);
// Polycyclic
G:=Group<a,b|a^67=b^3=1,b*a*b^-1=a^29>;
// generators/relations
Export
Subgroup lattice of C67⋊C3 in TeX
Character table of C67⋊C3 in TeX