Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#9090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #386 |
| commutator | C2×C4 | C22×C8×C59 |
| Frattini, cosocle | C2×C42 | C23×C59 |
| prime radical | C22×D4×C59 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,4,7,5,3,6,8)(9,10)(11,14)(12,20,23,18)(13,19)(15,17)(16,22,24,21)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3,4,8,5,2,6,7)(9,11,14,10,15,19,13,17)(12,18,21,16,23,20,22,24);(9,12,15,23)(10,16,17,24)(11,18,19,20)(13,22,14,21)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 2078);