Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#11893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#102 |
| commutator | C2×C8 | C22×C4×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C23×C4×C53 ◁ C23×C8×C53 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,7,8,5)(4,6)(9,10,14,19,16,21,15,20)(11,22,24,37,26,33,25,39)(12,27,29,38,13,31,30,18)(17,32,34,23,36,28,35,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3)(2,5)(4,8)(6,7)(9,11)(10,17)(12,28)(13,32)(14,25)(15,24)(16,26)(18,37)(19,35)(20,34)(21,36)(22,27)(23,29)(30,40)(31,33)(38,39);(3,8)(5,7)(9,12,14,29,16,13,15,30)(10,18,20,31,21,38,19,27)(11,23,24,28,26,40,25,32)(17,33,35,37,36,22,34,39)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 4881);