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×#25447 |
| 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 | |
892 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)(3,12,14,8,15,23,27,17)(5,19,20,9,21,24,30,18)(13,26,28,25,29,22,31,32)(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)(5,13,21,29)(6,14,16,27)(9,22)(10,12)(11,23)(18,26)(19,25)(20,28,30,31)(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)(23,27)(25,28)(26,29)(31,32);(1,5,16,30,7,21,6,20)(2,9,11,24,4,18,10,19)(3,13,27,31,15,29,14,28)(8,22,23,32,17,26,12,25)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 18435);