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G = C99order 99 = 32·11

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C99, also denoted Z99, SmallGroup(99,1)

Series: Derived Chief Lower central Upper central

C1 — C99
C1C3C33 — C99
C1 — C99
C1 — C99

Generators and relations for C99
 G = < a | a99=1 >


Smallest permutation representation of C99
Regular action on 99 points
Generators in S99
(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 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99)

G:=sub<Sym(99)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99)])

C99 is a maximal subgroup of   D99

99 conjugacy classes

class 1 3A3B9A···9F11A···11J33A···33T99A···99BH
order1339···911···1133···3399···99
size1111···11···11···11···1

99 irreducible representations

dim111111
type+
imageC1C3C9C11C33C99
kernelC99C33C11C9C3C1
# reps126102060

Matrix representation of C99 in GL2(𝔽199) generated by

280
0178
G:=sub<GL(2,GF(199))| [28,0,0,178] >;

C99 in GAP, Magma, Sage, TeX

C_{99}
% in TeX

G:=Group("C99");
// GroupNames label

G:=SmallGroup(99,1);
// by ID

G=gap.SmallGroup(99,1);
# by ID

G:=PCGroup([3,-3,-11,-3,99]);
// Polycyclic

G:=Group<a|a^99=1>;
// generators/relations

Export

Subgroup lattice of C99 in TeX

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