Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#33842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| prime radical | C61×#3283 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C4×D4×C61 ◁ C8×D4×C61 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 7808 |
A minimal faithful permutation representation — 4 generators on 97 points:
(1,2)(3,4)(5,6,11,8)(7,15,18,34)(9,22,26,33)(10,21,24,14)(12,29,19,17)(13,28,20,25)(16,35,27,31)(23,32,36,30)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(5,7,11,18)(6,12,8,19)(9,23,26,36)(10,27,24,16)(13,31,20,35)(14,32,21,30)(15,33,34,22)(17,28,29,25);(2,4)(5,8,11,6)(7,12,18,19)(9,20,26,13)(10,21,24,14)(15,29,34,17)(16,30,27,32)(22,25,33,28)(23,31,36,35);(5,9)(6,13)(7,16)(8,20)(10,28)(11,26)(12,30)(14,33)(15,34)(17,29)(18,27)(19,32)(21,22)(24,25)2623 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26830);