Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#13172 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #466 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C23×C59 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C59×#405 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2,4,3)(6,12)(7,16)(8,10)(9,22)(13,26)(14,30)(15,21)(17,23)(18,32)(19,31)(20,33)(24,28)(29,36)(34,35)(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);(1,3,4,2)(5,6)(7,13)(8,21)(9,14)(10,12)(11,15)(16,28)(17,27)(18,34)(19,24)(20,29)(22,25)(23,30)(26,32)(31,36)(33,35);(5,7,17,31,10,19,9,16,11,20,22,32,8,18,23,33)(6,13,27,36,12,24,14,28,15,29,25,26,21,34,30,35)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6160);