Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C53×#7946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#95 |
| commutator | C2×C4 | C2×C42×C53 |
| Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C25×C53 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C24×C4×C53 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2)(3,7,8,5)(4,6)(9,10)(11,18)(12,16)(13,22)(14,17)(15,19)(20,23)(21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(1,3)(2,5)(4,8)(6,7)(9,11)(10,15,17,24)(12,21)(13,19)(14,20)(16,18,22,23);(3,8)(5,7)(9,12,14,13)(10,16,17,22)(11,19,20,21)(15,23,24,18)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 934);