Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C27 |
| direct product | C2×C59×#2401 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C59 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C59 |
| socle | C24×C59 | C24 |
| prime radical | C25×C59 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C59 ◁ G | |
2294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 5 generators on 85 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(3,4)(5,8)(6,7)(9,10)(11,12,14,16)(13,15,17,18)(19,20)(21,23)(22,24)(25,26);(4,7)(8,10)(11,13,14,17)(12,15,16,18)(19,21,22,25)(20,23,24,26);(12,16)(15,18)(20,24)(21,25);(3,5,6,9)(4,8,7,10)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 27537);