Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#13150 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C59 | C2×D8 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2)(3,4)(5,6,8,7)(10,16)(11,20)(12,13)(14,22)(17,23)(18,24)(19,21)(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);(5,7,8,6)(9,10,17,21,14,19,12,16,15,20,13,18,22,24,23,11);(2,4)(9,11,12,19,22,18,17,10,15,16,23,24,14,21,13,20)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6138);