Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C2×C53×#1664 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C22×D4×C53 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C2×C42×C53 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 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);(56,57,61,65)(58,66,68,71)(59,64,60,63)(62,69,70,67)(74,80)(75,82)(77,85)(78,83)(81,84)(86,87);(56,58)(57,62)(59,69)(60,67)(61,68)(63,71)(64,66)(65,70)(72,73,76,79)(74,77,81,86)(75,83,82,78)(80,87,84,85);(56,58)(57,62)(59,67)(60,69)(61,68)(63,66)(64,71)(65,70)(72,74,76,81)(73,77,79,86)(75,84,82,80)(78,87,83,85)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11974);