Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9279 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#9291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #386 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2,3,7,5,8,4,6)(9,10)(11,19)(12,23,25,16)(13,26)(14,18)(15,21)(17,28)(20,33,36,40)(22,34)(24,31,27,32)(29,35,39,37)(30,38)(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);(2,6)(3,4)(7,8)(9,11,13,21,14,22,28,38)(10,15,17,19,18,30,26,34)(12,20,27,37,25,36,24,35)(16,29,32,33,23,39,31,40);(2,7)(3,4)(6,8)(9,12)(10,16)(11,20)(13,27)(14,25)(15,29)(17,32)(18,23)(19,33)(21,37)(22,36)(24,28)(26,31)(30,39)(34,40)(35,38)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2279);