Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C23×C4 |
| direct product | C53×#19670 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(3,10)(4,9)(5,7)(6,14)(8,13)(11,15)(12,16)(17,18,23,21)(19,27,30,25)(20,24,31,29)(22,32,28,26)(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);(2,7)(8,15)(9,14)(10,16)(17,19,28,31,23,30,22,20)(18,24,32,25,21,29,26,27);(1,3,6,13,5,12,4,11)(2,8,9,10,7,15,14,16)(17,20,22,30,23,31,28,19)(18,25,26,24,21,27,32,29);(1,4,5,6)(2,9,7,14)(3,11,12,13)(8,10,15,16)(17,21,23,18)(19,29,30,24)(20,25,31,27)(22,32,28,26)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12658);