Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22284 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C24×C4 |
| direct product | C53×#22284 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2328 |
| commutator | C2×C4 | C23×C4×C53 |
| Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#3154 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
796 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,8,13)(3,5,15,23)(4,16)(6,24,7,12)(9,25,22,11)(10,19)(14,26)(17,31)(18,32)(20,27)(21,30)(28,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3,7,25,8,15,6,11)(2,9,24,23,13,22,12,5)(4,17,19,28,21,32,20,14)(10,18,16,29,27,31,30,26);(1,4)(2,10,13,27)(3,14,15,28)(5,18)(6,19)(7,20)(8,21)(9,26)(11,17,25,32)(12,16,24,30)(22,29)(23,31);(1,5,6,22,8,23,7,9)(2,11,12,15,13,25,24,3)(4,18,19,29,21,31,20,26)(10,17,16,28,27,32,30,14)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 15272);