Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#11288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #120 |
| commutator | C24 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| socle | C22×C59 | #385 |
| prime radical | C24×C59 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(5,6,9,14,10,13,22,28)(7,11,17,25,16,24,20,29)(8,12,19,27,18,26,21,30)(15,23,32,34,31,35,33,36)(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);(1,2)(3,4)(5,7)(6,11,13,24)(8,15,18,31)(9,20)(10,16)(12,23)(14,29,28,25)(17,22)(19,33,21,32)(26,35)(27,36)(30,34);(2,4)(5,8)(6,12,13,26)(7,15,16,31)(9,21)(10,18)(11,23)(14,30,28,27)(17,33,20,32)(19,22)(24,35)(25,36)(29,34)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4276);