Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24 |
| direct product | C59×#23699 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C23×C59 | C22×D4 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ C22×C42×C59 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 87 points:
(5,6)(7,10)(8,9)(11,12)(13,14,17,20,16,18,24,27)(15,21,23,26,22,28,25,19)(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);(1,2)(3,4)(6,9)(10,12)(14,18)(19,26)(20,27)(21,28);(2,4)(13,15,16,22)(14,19,18,26)(17,25,24,23)(20,28,27,21);(5,7,8,11)(6,10,9,12)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16687);