Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C2×C4 |
| direct product | C61×#12521 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C61 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C61 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ C82×C61 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(18,22)(19,23)(20,26)(24,32)(25,30)(27,31)(28,29)(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);(17,18,23,29,20,24,27,30,21,25,31,32,26,28,19,22)4270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 5509);