Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C53 · Schur multiplier (H2) = C25 |
| direct product | C2×C53×#2151 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C53 | C23 |
| commutator | C22 | C23×C8×C53 |
| Frattini, cosocle | C2×C8 | C24×C53 |
| socle | C23×C53 | C22×C8 |
| prime radical | C24×C53 | C2×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C53 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(57,59)(60,61,63,67,64,68,73,79,65,69,74,80,75,81,85,89)(62,66,71,77,72,78,84,88,70,76,82,86,83,87,90,91);(56,57,58,59)(60,62)(61,66)(63,71)(64,72)(65,70)(67,77)(68,78)(69,76)(73,84)(74,82)(75,83)(79,88)(80,86)(81,87)(85,90)(89,91);(62,70)(66,76)(71,82)(72,83)(77,86)(78,87)(84,90)(88,91)5936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26384);