Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8674 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#8689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #380 |
| commutator | C42 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C23×C61 | C22⋊Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,6,9,7,4,5,15)(3,10,13,11,14,16,12,8)(17,18)(19,25)(20,22)(21,29)(23,27)(24,28)(26,32)(30,31)(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);(1,3,6,13,7,14,5,12)(2,8,15,16,4,11,9,10)(18,22)(23,31)(24,29)(25,32);(1,4)(2,7)(3,11)(5,15)(6,9)(8,14)(10,13)(12,16)(17,19,20,26)(18,23,22,31)(21,30,28,27)(24,32,29,25)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1677);