Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#17521 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C22×D4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| socle | C22×C59 | C22×C22⋊C4 |
| prime radical | C59×#3481 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C4×#41×C59 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,10)(4,6)(5,9)(7,11)(8,13)(12,15)(14,16)(17,18,21,25,22,24,20,29)(19,26,27,23,28,32,30,31)(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);(2,6)(4,13)(7,14)(8,9)(10,15)(12,16)(17,19)(18,23)(20,30)(21,27)(22,28)(24,31)(25,32)(26,29);(1,3)(2,7)(4,12)(5,11)(6,14)(8,15)(9,10)(13,16)(18,24)(23,31)(25,29)(26,32);(3,11)(7,10)(12,16)(14,15)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10509);