Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#19717 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C2×#127×C61 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,6)(4,11)(7,12)(8,13)(10,15)(14,16)(17,18)(19,24)(20,29)(21,31)(22,26)(23,28)(25,30)(27,32)(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);(1,2,4,6,5,8,11,13)(3,7,10,12,9,14,15,16)(17,19,21,28,22,27,30,20)(18,23,25,24,26,29,31,32);(1,3,5,9)(2,7,8,14)(4,10,11,15)(6,12,13,16)(17,20,30,27,22,28,21,19)(18,24,31,23,26,32,25,29);(3,9)(7,14)(10,15)(12,16)(19,27)(20,28)(23,29)(24,32)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12705);