Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61214 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3497 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2,4,6)(3,7,8,5)(9,10,14,18)(11,19,22,32)(12,23,24,16)(13,26,28,17)(15,27,30,21)(20,34,35,33)(25,31,39,38)(29,36,37,40)(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)(12,24)(16,23)(20,35)(25,39)(29,37)(31,38)(33,34)(36,40);(9,11,14,22)(10,15,18,30)(12,20,24,35)(13,27,28,21)(16,29,23,37)(17,32,26,19)(25,40,39,36)(31,34,38,33);(3,8)(5,7)(12,24)(16,23)(20,35)(25,39)(29,37)(31,38)(33,34)(36,40);(9,12)(10,16)(11,20)(13,25)(14,24)(15,29)(17,31)(18,23)(19,33)(21,36)(22,35)(26,38)(27,40)(28,39)(30,37)(32,34)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54202);