Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#8528 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #379 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C53×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 93 points:
(2,6)(3,4)(7,8)(9,10)(11,19,22,32)(12,23,25,16)(13,17)(14,18)(15,21,30,26)(20,35)(24,33,27,31)(28,34)(29,36)(37,40)(38,39)(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);(1,2)(3,8)(4,6)(5,7)(9,11)(10,15)(12,20)(13,26)(14,22)(16,29)(17,32)(18,30)(19,34)(21,28)(23,39)(24,38)(25,37)(27,36)(31,35)(33,40);(1,2)(3,6)(4,8)(5,7)(9,12)(10,16)(11,20)(13,27)(14,25)(15,29)(17,33)(18,23)(19,35)(21,38)(22,37)(24,28)(26,36)(30,39)(31,34)(32,40)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1516);