Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C29 |
| direct product | C53×#61110 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
2684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 5 generators on 69 points:
(1,2,6,8)(3,10,12,14)(4,7,15,13)(5,11,16,9)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69);(1,3)(2,4)(5,7)(6,12)(8,15)(9,14)(10,11)(13,16);(1,4)(2,3)(5,10)(6,15)(7,11)(8,12)(9,13)(14,16);(1,4)(2,7)(3,11)(5,14)(6,15)(8,13)(9,12)(10,16);(2,8)(3,12)(7,13)(9,11)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 54098);