Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#9929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C53 |
| prime radical | C24×C53 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C23×C4×C53 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,2)(3,4)(5,6)(7,10)(8,11)(9,12)(13,16)(14,17)(15,19)(18,20)(21,22,26,29)(23,30,32,35)(24,28,25,33)(27,34,36,31)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,7,9,14)(6,10,12,17)(8,13,15,20)(11,18,19,16)(21,23,26,32)(22,27,29,36)(24,31,25,34)(28,35,33,30);(2,4)(5,8)(6,11)(7,13)(9,15)(10,16)(12,19)(14,20)(17,18)(21,24,26,25)(22,28,29,33)(23,31,32,34)(27,35,36,30)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2917);