Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#18729 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3205 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
940 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(3,11)(4,9)(5,8)(6,10)(7,13)(12,16)(14,15)(18,23)(20,21)(24,30)(25,29)(26,28)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(1,3)(2,7)(4,12)(5,13)(6,14)(8,15)(9,11)(10,16)(17,18,22,25)(19,24,27,32)(20,23,21,29)(26,31,28,30);(2,8)(4,5)(7,15)(9,10)(11,16)(12,13)(17,19)(18,24)(20,28)(21,26)(22,27)(23,30)(25,32)(29,31);(1,4,6,5)(2,8,10,9)(3,12,14,13)(7,15,16,11)(17,20,22,21)(18,23,25,29)(19,26,27,28)(24,31,32,30)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11717);