Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #29902 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#29903 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #2622 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×H(5,𝔽2)×C61 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C4×C61 ◁ G | |
756 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,12)(4,17)(5,22)(6,10)(7,11)(8,14)(9,19)(13,30)(15,24)(16,29)(18,23)(20,26)(21,27)(25,31)(28,32)(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);(1,3,5,15,7,14,6,16)(2,8,10,24,11,12,22,29)(4,18,19,13,21,32,20,31)(9,25,17,28,26,30,27,23);(1,4,7,21)(2,9,11,26)(3,13,14,31)(5,20,6,19)(8,23,12,28)(10,27,22,17)(15,18,16,32)(24,30,29,25);(1,2)(3,8)(4,9)(5,10)(6,22)(7,11)(12,14)(13,28)(15,24)(16,29)(17,19)(18,25)(20,27)(21,26)(23,31)(30,32)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22891);