Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#19417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C2×#41×C61 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(17,18,22,26)(19,23,28,32)(20,25,21,30)(24,29,31,27)(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);(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9)(17,19)(18,23)(20,29)(21,27)(22,28)(24,30)(25,31)(26,32);(17,19)(18,24)(20,27)(21,29)(22,28)(23,30)(25,32)(26,31);(17,20,22,21)(18,25,26,30)(19,27,28,29)(23,24,32,31)2989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12405);