Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7529 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C61 · Schur multiplier (H2) = C4 |
| direct product | C61×#7532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #1408 |
| commutator | C4×C8 | C2×C4×C61 |
| Frattini, cosocle | #494 | C22×C61 |
| prime radical | C22×C61 | #353 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C22×C61 ◁ C2×C4×C61 ◁ C42×C61 ◁ C61×#494 ◁ G | |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 2 generators on 93 points:
(1,2,5,11,8,13,3,14)(4,10,19,26,22,29,18,9)(6,12,16,27,7,24,17,30)(15,31,20,28,23,25,21,32)(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);(1,3,8,5)(2,9,13,26)(4,18,22,19)(6,17,7,16)(10,27,29,30)(11,28,14,32)(12,31,24,25)(15,21,23,20)1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 520);