Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#25142 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(3,4)(5,6,9,13,10,14,23,30)(7,11,16,25,17,26,34,36)(8,18,20,28,21,29,22,12)(15,31,32,27,19,35,33,24)(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);(2,4)(5,7,9,16,10,17,23,34)(6,11,13,25,14,26,30,36)(8,19,20,33,21,15,22,32)(12,27,18,35,28,24,29,31);(5,8,10,21)(6,12,14,28)(7,15,17,19)(9,22,23,20)(11,24,26,27)(13,29,30,18)(16,33,34,32)(25,35,36,31);(2,4)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18130);