Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #29751 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#29889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| prime radical | C2×#41×C61 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
596 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,7)(4,8)(5,6)(9,15)(10,13)(11,16)(12,14)(17,18,20,26,22,25,21,24)(19,23,28,31,29,30,27,32)(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);(2,6)(7,13)(8,14)(15,16)(17,19)(18,23)(20,28)(21,27)(22,29)(24,32)(25,30)(26,31);(1,3,5,10)(2,7,6,13)(4,11,12,9)(8,16,14,15)(18,24)(19,27)(20,21)(23,30)(25,26)(28,29);(1,4,5,12)(2,8,6,14)(3,9,10,11)(7,15,13,16)(18,25)(23,30)(24,26)(31,32)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 22877);