Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#61204 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C53×#532 ◁ G | |
2032 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)(11,16)(12,22)(13,18)(14,27)(15,19)(17,20)(21,30)(23,36)(24,29)(25,33)(26,34)(28,32)(31,35)(37,40)(38,39)(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)(2,5)(4,8)(6,7)(9,11,15,14)(10,16,19,27)(12,20,24,28)(13,25,26,21)(17,29,32,22)(18,33,34,30)(23,37,38,35)(31,36,40,39);(9,12,15,24)(10,17,19,32)(11,20,14,28)(13,23,26,38)(16,29,27,22)(18,31,34,40)(21,35,25,37)(30,39,33,36);(3,8)(5,7)(13,26)(18,34)(21,25)(23,38)(30,33)(31,40)(35,37)(36,39);(9,13)(10,18)(11,21)(12,23)(14,25)(15,26)(16,30)(17,31)(19,34)(20,35)(22,36)(24,38)(27,33)(28,37)(29,39)(32,40)2915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54192);