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×#18744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3212 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(2,7)(3,10)(4,5)(9,13)(11,12)(14,15)(18,23)(19,21)(20,27)(24,31)(25,29)(30,32)(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);(1,2,6,9)(3,8,12,16)(4,7,5,13)(10,14,11,15)(17,18,22,25)(19,23,21,29)(20,24,27,32)(26,30,28,31);(1,3,6,12)(2,8,9,16)(4,10,5,11)(7,14,13,15)(17,19,22,21)(18,23,25,29)(20,28,27,26)(24,31,32,30);(1,4,6,5)(2,7,9,13)(3,11,12,10)(8,15,16,14)(17,20)(18,24)(19,26)(21,28)(22,27)(23,30)(25,32)(29,31)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11732);