Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#33744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ #117×C61 ◁ C61×#405 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,6)(4,5)(7,8)(11,19)(12,21)(13,24)(15,26)(17,27)(18,30)(20,31)(22,38)(23,34)(25,37)(28,40)(29,35)(32,33)(36,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(2,5)(6,8)(9,10)(11,20)(12,17)(13,18)(14,16)(15,23)(19,31)(21,27)(22,36)(24,30)(25,29)(26,34)(28,32)(33,40)(35,37)(38,39);(9,11,21,33,13,22,25,34,14,23,37,38,24,32,12,19)(10,15,27,39,18,28,29,31,16,20,35,40,30,36,17,26);(1,3,4,7)(2,6,5,8)(10,16)(15,20)(17,29)(18,30)(26,31)(27,35)(28,36)(39,40)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26732);