Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D82 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#20007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C2×D4×C61 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,7,4)(3,11,14,16)(5,10,6,9)(8,15,12,13)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)(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);(1,3,7,14)(2,8,4,12)(5,13,6,15)(9,11,10,16);(1,4,7,2)(3,12,14,8)(5,10,6,9)(11,13,16,15)(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25);(1,5)(2,9)(4,10)(6,7)(11,16)(13,15)2989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12995);