Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9758 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C2×C4 |
| direct product | C53×#9765 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #390 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C23×C53 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
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)(17,18,22,27,23,26,21,36)(19,24,30,40,29,41,37,39)(20,31,34,43,35,47,33,25)(28,44,45,38,32,46,48,42)(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)(18,24,27,39,26,41,36,40)(20,32,33,48,35,28,34,45)(25,42,31,46,43,38,47,44);(3,11)(7,15)(10,16)(12,13)(17,20,21,33,23,35,22,34)(18,25,27,31,26,43,36,47)(19,28,30,45,29,32,37,48)(24,38,39,44,41,42,40,46)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2753);