Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C53×#1307 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #95 |
| commutator | C23 | C2×C42×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C24×C53 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 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);(56,57,59,62,60,61,63,58)(64,65,67,70,68,71,75,78)(66,72,74,79,73,69,76,77);(56,58,59,61,60,62,63,57)(64,66)(65,69,71,72)(67,74)(68,73)(70,77,78,79)(75,76)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1105);