Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#12868 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×D8 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C24×C59 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C23×C4×C59 ◁ C23×C8×C59 ◁ G | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 87 points:
(1,2,3,4)(5,6)(7,10)(8,9)(11,12)(14,18)(15,21)(17,24)(19,27)(20,23)(22,28)(25,26)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(6,9)(10,12)(13,14,16,18)(15,19,22,26)(17,20,23,24)(21,25,28,27);(5,7,8,11)(6,10,9,12)(13,15,16,22)(14,19,18,26)(17,25,23,27)(20,28,24,21)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5856);