Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#11956 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | #333 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| socle | C2×C61 | C2×#333 |
| prime radical | C23×C61 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ C22×C4×C61 ◁ C2×C4×C8×C61 ◁ G | |
292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,5,9,18,10,28,26,6,11,20,27,4,8,17,24)(3,12,15,25,13,23,19,31,14,29,30,32,16,7,21,22)(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);(1,3,6,14)(2,7)(4,13,18,16)(5,19,20,21)(8,12)(9,25)(10,29)(11,23)(15,17,30,28)(22,26)(24,31)(27,32);(1,4,6,18)(2,8,11,10)(3,13,14,16)(5,17,20,28)(7,12,23,29)(9,24,27,26)(15,19,30,21)(22,25,31,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4944);