Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24×C8 |
| direct product | C2×C53×#1709 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C2×C53×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 79 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);(57,62)(58,63)(59,60)(64,65)(66,72)(67,75)(68,70)(69,73)(71,76)(74,78)(77,79);(56,57,60,58,61,63,59,62)(64,66,67,73,68,74,76,79)(65,69,71,72,70,77,75,78);(56,58,59,57,61,62,60,63)(65,70)(69,77)(71,75)(72,78)4028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12585);