Copied to
clipboard

G = C77order 77 = 7·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C77, also denoted Z77, SmallGroup(77,1)

Series: Derived Chief Lower central Upper central

C1 — C77
C1C11 — C77
C1 — C77
C1 — C77

Generators and relations for C77
 G = < a | a77=1 >


Smallest permutation representation of C77
Regular action on 77 points
Generators in S77
(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 68 69 70 71 72 73 74 75 76 77)

G:=sub<Sym(77)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)])

C77 is a maximal subgroup of   D77

77 conjugacy classes

class 1 7A···7F11A···11J77A···77BH
order17···711···1177···77
size11···11···11···1

77 irreducible representations

dim1111
type+
imageC1C7C11C77
kernelC77C11C7C1
# reps161060

Matrix representation of C77 in GL1(𝔽463) generated by

277
G:=sub<GL(1,GF(463))| [277] >;

C77 in GAP, Magma, Sage, TeX

C_{77}
% in TeX

G:=Group("C77");
// GroupNames label

G:=SmallGroup(77,1);
// by ID

G=gap.SmallGroup(77,1);
# by ID

G:=PCGroup([2,-7,-11]);
// Polycyclic

G:=Group<a|a^77=1>;
// generators/relations

Export

Subgroup lattice of C77 in TeX

׿
×
𝔽