Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C53×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
1318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,3,4)(5,6)(7,16)(8,20)(9,14)(10,15)(11,18)(12,21)(13,25)(17,26)(19,27)(22,29)(23,30)(24,28)(31,32)(33,35)(34,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,7,10,19)(6,11,15,28)(8,17,23,34)(9,24,25,18)(12,26,29,36)(13,27,14,16)(20,31,30,35)(21,33,22,32);(2,4)(5,6)(7,16)(8,12)(9,13)(10,15)(11,24)(14,25)(17,31)(18,28)(19,27)(20,21)(22,30)(23,29)(26,32)(33,36)(34,35);(5,8,10,23)(6,12,15,29)(7,17,19,34)(9,22,25,21)(11,26,28,36)(13,30,14,20)(16,31,27,35)(18,33,24,32)2279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 17449);