Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#17680 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| prime radical | C59×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C4×#41×C59 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,9,11,16)(4,8)(5,7)(6,10,14,12)(13,15)(17,18,22,25,23,19,21,27)(20,26,30,32,28,24,29,31)(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);(1,3)(2,6)(4,12)(5,11)(7,14)(8,16)(9,15)(10,13)(17,19,23,18)(20,26,28,24)(21,25,22,27)(29,31,30,32);(2,7)(6,14)(8,15)(9,16)(17,20)(18,24)(19,26)(21,29)(22,30)(23,28)(25,31)(27,32);(20,28)(24,26)(29,30)(31,32)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10668);