Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#11978 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×#102 |
| commutator | C2×C8 | C22×C4×C61 |
| Frattini, cosocle | C4×C8 | C23×C61 |
| prime radical | C61×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 3 generators on 101 points:
(2,6)(3,4)(7,8)(9,10,12,18,26,32,39,34,13,16,27,17,14,19,28,36)(11,20,22,37,29,35,25,30,23,38,21,31,24,33,40,15)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2)(3,6)(4,8)(5,7)(9,11)(10,15)(12,25)(13,23)(14,29)(16,30)(17,33)(18,35)(19,37)(20,34)(21,28)(22,39)(24,26)(27,40)(31,32)(36,38);(1,3,5,4)(2,6,7,8)(10,16)(15,30)(17,18)(19,32)(20,38)(31,37)(33,35)(34,36)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 4966);