Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#9531 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #386 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | #121×C61 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
412 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,5,9,6,10,4,7)(3,11,13,8,14,15,12,16)(17,18,21,25,22,19,23,27)(20,26,29,32,28,24,30,31)(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);(2,7,10,9)(8,11,16,15)(17,19,21,27,22,18,23,25)(20,26,30,31,28,24,29,32);(1,3)(2,8)(4,12)(5,13)(6,14)(7,11)(9,15)(10,16)(17,20)(18,24)(19,26)(21,30)(22,28)(23,29)(25,32)(27,31)2257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 2519);