Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#19916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C61 |
| prime radical | C61×#1625 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,6)(4,13)(7,14)(8,9)(10,15)(11,16)(17,18,21,25)(19,22,27,31)(20,23,28,24)(26,29,32,30)(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);(1,2,5,9)(3,10,12,7)(4,8,13,6)(11,14,16,15)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(1,3,5,12)(2,7,9,10)(4,11,13,16)(6,14,8,15)(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(2,8)(4,13)(6,9)(7,15)(10,14)(11,16)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 12904);