Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#33595 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C2×#459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C61×#405 ◁ G | |
706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,7)(3,11)(4,15)(5,16)(8,22)(9,20)(10,26)(12,17)(13,28)(14,29)(18,30)(19,24)(23,27)(25,32)(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);(1,2,4,7,6,9,15,20)(3,8,12,19,14,23,13,25)(5,10,16,21,18,26,30,31)(11,24,28,22,29,32,17,27);(1,3)(2,8)(4,12)(5,17)(6,14)(7,19)(9,23)(10,27)(11,16)(13,15)(18,28)(20,25)(21,24)(22,26)(29,30)(31,32);(2,9)(7,20)(8,23)(10,26)(19,25)(21,31)(22,27)(24,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26583);