Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17411 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C61×#17412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C61 |
| Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×#120×C61 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×#117×C61 ◁ G | |
1046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,9,6,10,15,22)(3,8,12,21,11,20,23,30)(5,7,14,18,16,19,26,29)(13,17,25,28,24,27,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,7)(4,14)(8,17)(10,19)(12,25)(15,26)(20,27)(23,31);(1,3,5,13)(2,8,7,17)(4,12,14,25)(6,11,16,24)(9,21,18,28)(10,20,19,27)(15,23,26,31)(22,30,29,32);(3,11)(8,20)(12,23)(13,24)(17,27)(21,30)(25,31)(28,32)3355 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 10400);