Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C53×#33708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C53×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ C2×C4×C8×C53 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,5)(4,6)(7,8)(9,10)(11,24)(12,18)(13,20)(14,33)(15,34)(16,35)(17,23)(19,28)(21,25)(22,32)(26,37)(27,38)(29,36)(30,40)(31,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,4,7)(2,5,6,8)(9,11,25,29,16,26,32,31,17,28,15,27,13,30,14,12)(10,18,33,40,20,38,34,19,23,39,22,37,35,36,21,24);(2,6)(5,8)(9,12,14,30,13,27,15,28,17,31,32,26,16,29,25,11)(10,19,21,38,35,40,22,18,23,24,34,36,20,37,33,39);(9,13,17,16)(10,20,23,35)(11,26,28,30)(12,29,31,27)(14,15,32,25)(18,36,39,38)(19,40,24,37)(21,33,34,22)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26696);