Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#12826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #1804 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C22×C8 | C23×C61 |
| prime radical | C22×D8×C61 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ C61×#405 ◁ G | |
412 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)(3,13,16,30)(4,10)(5,9)(6,22)(7,12)(8,14,25,17)(11,20)(15,28,19,24)(18,26)(21,27)(23,32,29,31)(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);(1,3)(2,8,12,25)(4,14)(5,19)(6,17)(7,16)(9,23,27,29)(10,13,22,30)(11,28,26,24)(15,21)(18,32)(20,31);(2,9)(4,6)(5,20)(8,23)(10,11)(12,27)(13,28)(14,17)(15,32)(18,21)(19,31)(22,26)(24,30)(25,29)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5814);