Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #29610 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#29707 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C61×#3460 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 85 points:
(2,3)(6,7)(9,10)(11,17)(12,14)(13,21)(15,19)(16,20)(18,24)(22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,2)(3,5)(4,6)(7,8)(10,14)(13,20)(17,24)(19,22);(1,3,5,2)(4,6,8,7)(9,11,12,18)(10,15,14,23)(13,22,20,19)(16,24,21,17);(1,4,5,8)(2,6,3,7)(11,18)(15,23)(17,24)(19,22)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22695);