Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C61×#33732 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C23×C61 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,4,6)(3,7,8,5)(9,10,12,15)(11,19,21,33)(13,26,24,39)(14,27,25,18)(16,30,28,22)(17,32,29,20)(23,38,37,35)(31,36,34,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3,4,8)(2,5,6,7)(10,15)(16,28)(17,29)(18,27)(19,33)(26,39)(31,34)(35,38);(9,11,20,36,14,23,24,30,12,21,32,40,25,37,13,22)(10,16,26,35,18,31,29,33,15,28,39,38,27,34,17,19);(11,21)(16,28)(19,33)(22,30)(23,37)(31,34)(35,38)(36,40)3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26720);