Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#12940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #447 |
| commutator | C2×C8 | C22×C4×C53 |
| Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C22×D8×C53 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C53×#405 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 89 points:
(1,2,4,3)(5,6)(7,17)(8,14)(9,13)(10,26)(11,16)(12,18)(15,23)(19,30)(20,29)(21,35)(22,34)(24,33)(25,32)(27,28)(31,36)(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);(1,3,4,2)(5,7)(6,12)(8,22)(9,18)(10,27)(11,21)(13,28)(14,17)(15,34)(16,31)(19,24)(20,23)(25,36)(26,30)(29,32)(33,35);(6,13)(8,9)(10,23)(12,28)(14,26)(15,33)(16,32)(17,30)(18,22)(19,36)(20,27)(24,25)(29,31)(34,35)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 5928);