Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C53 · Schur multiplier (H2) = C4 |
| direct product | C53×#13106 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C53 | C2×D4 |
| commutator | C2×C4 | C22×C8×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| socle | C22×C53 | C8×D4 |
| prime radical | C23×C53 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C53 ◁ C22×C16×C53 ◁ G | |
272 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)(3,6)(4,5)(7,8)(9,10,14,19,13,20,30,38,15,21,32,22,31,18,36,37)(11,16,24,33,23,27,17,34,25,12,26,28,39,29,35,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,8)(9,11,14,24,13,23,30,17,15,25,32,26,31,39,36,35)(10,16,19,33,20,27,38,34,21,12,22,28,18,29,37,40);(1,3,4,7)(2,6,5,8)(9,12)(10,17)(11,22)(13,29)(14,28)(15,16)(18,24)(19,25)(20,26)(21,35)(23,37)(27,31)(30,40)(32,33)(34,36)(38,39)4028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6094);