Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#8325 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #379 |
| commutator | C22×C4 | C22×C4×C61 |
| Frattini, cosocle | C2×C42 | C23×C61 |
| prime radical | C2×#121×C61 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
748 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,10,12,7)(4,6)(5,9)(8,13)(11,15,16,14)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32)(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);(2,6)(4,13)(7,14)(8,9)(10,15)(11,16)(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(1,3)(2,7)(4,11)(5,12)(6,14)(8,15)(9,10)(13,16)(19,25)(22,28)(26,31)(29,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1313);