Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#12986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | #386 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C2×C53 | #1869 |
| prime radical | C2×#135×C53 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C8×C53 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,7,11,6,10,24,15,8,12,26,30,5,23,14,31)(3,13,9,27,17,22,28,25,18,20,29,32,16,4,19,21)(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);(1,3,14,19,5,16,26,29,8,18,24,28,6,17,7,9)(2,4,15,27,23,20,11,21,12,22,31,32,10,13,30,25);(1,4)(2,9)(3,15)(5,20)(6,13)(7,25)(8,22)(10,28)(11,16)(12,29)(14,27)(17,30)(18,31)(19,23)(21,26)(24,32)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 5974);