Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#9875 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C61 | C2×D4 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| socle, prime radical | C23×C61 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C61 ◁ C43×C61 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,7)(4,5)(6,8)(9,10,14,15,13,16,12,11)(17,18)(19,25)(20,29)(21,23)(22,27)(24,26)(28,31)(30,32)(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);(2,5)(6,7)(9,11,12,16,13,15,14,10)(17,19,26,32,21,28,20,27)(18,22,29,31,23,30,24,25);(1,3,4,8)(2,6,5,7)(9,12,13,14)(10,15,16,11)(18,23)(22,30)(24,29)(25,31)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 2863);