Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C53×#2164 |
| 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 | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 95 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);(56,57)(58,61)(59,60)(62,63)(64,65,67,71,68,72,77,83,69,73,78,84,79,85,89,93)(66,70,75,81,76,82,88,92,74,80,86,90,87,91,94,95);(57,60)(61,63)(64,66)(65,70)(67,75)(68,76)(69,74)(71,81)(72,82)(73,80)(77,88)(78,86)(79,87)(83,92)(84,90)(85,91)(89,94)(93,95);(56,58,59,62)(57,61,60,63)(66,74)(70,80)(75,86)(76,87)(81,90)(82,91)(88,94)(92,95)5936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26405);