Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#25446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2428 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,6,11,7,4,16,10)(3,12,14,8,15,23,29,17)(5,19,20,9,21,24,30,18)(13,26,27,25,28,22,31,32)(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);(1,3,7,15)(2,8)(4,17)(5,13,21,28)(6,14,16,29)(9,22)(10,12)(11,23)(18,26)(19,25)(20,27,30,31)(24,32);(1,4)(2,7)(3,8)(5,18)(6,11)(9,21)(10,16)(12,14)(13,22)(15,17)(19,30)(20,24)(23,29)(25,27)(26,28)(31,32);(1,5,6,20,7,21,16,30)(2,9,10,19,4,18,11,24)(3,13,14,27,15,28,29,31)(8,22,12,25,17,26,23,32)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18434);