Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#8032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C24×C59 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G | |
566 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2,3,4)(5,6)(7,13)(8,16)(9,12)(10,15)(11,17)(14,19)(18,20)(21,22)(23,30)(24,28)(25,34)(26,29)(27,32)(31,36)(33,35)(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);(5,7)(6,10,12,18)(8,15)(9,14)(11,13,16,19)(17,20)(21,23,25,33,26,32,24,31)(22,27,28,35,29,30,34,36);(7,14)(10,18)(13,19)(15,20)(21,24,26,25)(22,28,29,34)(23,31,32,33)(27,35,30,36)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 1020);