Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#60713 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3058 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×#41×C53 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,16)(12,22)(13,18)(14,28)(15,19)(17,24)(20,31)(21,29)(23,35)(25,36)(26,32)(27,33)(30,37)(34,40)(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);(2,5)(6,8)(9,11,15,14)(10,16,19,28)(12,20,25,24)(13,26,27,21)(17,22,31,36)(18,32,33,29)(23,37,38,34)(30,39,40,35);(9,12,14,24,15,25,11,20)(10,17,16,22,19,31,28,36)(13,23,26,37,27,38,21,34)(18,30,29,35,33,40,32,39);(1,3,4,7)(2,6,5,8)(13,27)(18,33)(21,26)(23,38)(29,32)(30,40)(34,37)(35,39);(9,13)(10,18)(11,21)(12,23)(14,26)(15,27)(16,29)(17,30)(19,33)(20,34)(22,35)(24,37)(25,38)(28,32)(31,40)(36,39)3392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53701);