direct product, cyclic, abelian, monomial
Aliases: C48, also denoted Z48, SmallGroup(48,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C48 |
| C1 — C48 |
| C1 — C48 |
Generators and relations for C48
G = < a | a48=1 >
Smallest permutation representation of C48
►Regular action on 48 points
Generators in S48
(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)
G:=sub<Sym(48)| (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)>;
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) );
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)]])
C48 is a maximal subgroup of
C3⋊C32 D6.C8 D48 C48⋊C2 Dic24 C16.A4 C7⋊C48 He3⋊2C16
C48 is a maximal quotient of
C7⋊C48
48 conjugacy classes
| class | 1 | 2 | 3A | 3B | 4A | 4B | 6A | 6B | 8A | 8B | 8C | 8D | 12A | 12B | 12C | 12D | 16A | ··· | 16H | 24A | ··· | 24H | 48A | ··· | 48P |
| order | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 6 | 8 | 8 | 8 | 8 | 12 | 12 | 12 | 12 | 16 | ··· | 16 | 24 | ··· | 24 | 48 | ··· | 48 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
48 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | ||||||||
| image | C1 | C2 | C3 | C4 | C6 | C8 | C12 | C16 | C24 | C48 |
| kernel | C48 | C24 | C16 | C12 | C8 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 2 | 2 | 4 | 4 | 8 | 8 | 16 |
Matrix representation of C48 ►in GL2(𝔽7) generated by
| 0 | 2 |
| 2 | 5 |
G:=sub<GL(2,GF(7))| [0,2,2,5] >;
C48 in GAP, Magma, Sage, TeX
C_{48} % in TeX
G:=Group("C48"); // GroupNames label
G:=SmallGroup(48,2);
// by ID
G=gap.SmallGroup(48,2);
# by ID
G:=PCGroup([5,-2,-3,-2,-2,-2,30,42,58]);
// Polycyclic
G:=Group<a|a^48=1>;
// generators/relations
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