Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C22 |
| direct product | C2×C53×#1366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #333 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C4×C8 | C23×C53 |
| prime radical | C23×C53 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×C4×C8×C53 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 87 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);(56,57,59,64,72,65,83,81,61,66,74,82,60,63,73,79)(58,67,69,80,75,78,71,86,68,84,85,87,70,62,76,77);(56,58,61,68)(57,62)(59,71,74,76)(60,75,72,70)(63,67)(64,80)(65,84)(66,78)(69,73,85,83)(77,81)(79,86)(82,87)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 4943);