Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#33842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| prime radical | C53×#3283 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×D4×C53 ◁ C8×D4×C53 ◁ G | |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2)(3,4)(5,6,12,17)(7,18,22,34)(8,14,11,28)(9,25,26,10)(13,29,31,20)(15,16,24,23)(19,33,21,36)(27,32,35,30)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,7,12,22)(6,13,17,31)(8,21,11,19)(9,18,26,34)(10,27,25,35)(14,32,28,30)(15,20,24,29)(16,33,23,36);(2,4)(5,8,12,11)(6,14,17,28)(7,19,22,21)(9,23,26,16)(10,24,25,15)(13,30,31,32)(18,33,34,36)(20,35,29,27);(5,9)(6,15)(7,13)(8,23)(10,14)(11,16)(12,26)(17,24)(18,27)(19,30)(20,33)(21,32)(22,31)(25,28)(29,36)(34,35)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26830);