Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#12989 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | #386 |
| commutator | C23 | C22×C8×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C2×C53 | #1869 |
| prime radical | C53×#525 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C8×C53 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,4,9,5,10,17,24,6,8,18,15,19,22,30,28)(3,11,13,23,14,25,27,32,12,7,16,20,26,21,29,31)(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);(1,2,4,15,5,10,17,28,6,8,18,9,19,22,30,24)(3,7,16,20,14,21,29,31,12,11,13,23,26,25,27,32);(1,3)(2,7)(4,16)(5,14)(6,12)(8,11)(9,23)(10,21)(13,18)(15,20)(17,29)(19,26)(22,25)(24,32)(27,30)(28,31)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 5977);