Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C61×#2249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C22×D16×C61 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(4,6)(7,8)(9,17)(10,22)(11,14)(12,25)(13,19)(15,18)(16,23)(20,29)(21,36)(24,37)(26,35)(27,38)(28,33)(30,32)(31,34);(7,9,18,32,12,21,24,35,11,20,33,38,23,34,10,19)(8,13,22,31,16,27,28,29,14,26,37,36,25,30,15,17);(3,4,5,6)(8,14)(13,26)(15,28)(16,25)(17,29)(22,37)(27,30)(31,36)4636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26700);