Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C23 |
| direct product | C61×#10016 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C61 |
| socle | C22×C61 | #392 |
| prime radical | C22×D4×C61 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C2×C42×C61 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(17,18,22,26)(19,27,30,31)(20,25,21,24)(23,29,32,28)(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);(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,19,22,30)(18,23,26,32)(20,29,21,28)(24,31,25,27);(6,15)(9,16)(18,24)(20,21)(23,31)(25,26)(27,32)(28,29)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 3004);