Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#9314 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #386 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C2×#41×C53 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2,5,8,6,9,4,14)(3,10,13,15,11,16,12,7)(17,18,22,27,23,26,21,35)(19,24,30,40,29,41,37,39)(20,31,33,25,34,44,36,43)(28,45,47,42,32,48,46,38)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3,6,11)(2,7)(4,12,5,13)(8,10)(9,15)(14,16)(17,19,21,30,23,29,22,37)(18,24,27,39,26,41,35,40)(20,32,36,46,34,28,33,47)(25,42,44,45,43,38,31,48);(3,11)(7,15)(10,16)(12,13)(17,20)(18,25)(19,28)(21,36)(22,33)(23,34)(24,38)(26,43)(27,44)(29,32)(30,47)(31,35)(37,46)(39,48)(40,45)(41,42)1961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2302);