Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C61 · Schur multiplier (H2) = C28 |
| direct product | C61×#61800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C61 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C61×#532 ◁ G | |
1730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(18,24)(19,27)(21,23)(25,32)(28,29)(30,31)(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)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,18,22,24)(19,28,30,25)(20,23,26,21)(27,32,31,29);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,19,22,30)(18,25,24,28)(20,29,26,32)(21,27,23,31);(3,11)(6,9)(10,16)(13,15)(17,20,22,26)(18,21,24,23)(19,29,30,32)(25,27,28,31);(2,8)(6,9)(7,14)(13,15)(17,21,22,23)(18,26,24,20)(19,27,30,31)(25,32,28,29)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 54788);