Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C22×C61×D32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | D16 |
| commutator, Frattini, cosocle | C16 | C24×C61 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×C4×C61 ◁ C22×C8×C61 ◁ C22×C16×C61 ◁ G | |
542 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)(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);(3,4);(5,6)(7,11)(8,20)(9,23)(10,15)(12,16)(13,17)(14,21)(18,30)(19,26)(22,36)(24,32)(25,31)(27,35)(28,33)(29,34);(6,11)(7,16)(8,17)(9,21)(12,13)(14,30)(15,26)(18,35)(19,33)(20,24)(22,34)(23,25)(27,36)(28,29)(31,32)4636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26963);