Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#13400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C53 |
| prime radical | C53×#3060 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(3,12)(4,17)(5,9)(6,11)(7,15)(8,21)(10,20)(13,30)(14,28)(16,26)(18,32)(19,25)(22,27)(23,29)(24,31)(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);(1,2)(3,13)(4,18)(5,10)(6,11)(7,16)(8,22)(9,20)(12,19)(14,25)(15,29)(17,32)(21,27)(23,24)(26,31)(28,30);(1,3,5,23,6,14,20,16)(2,7,10,13,11,24,9,25)(4,19,21,31,22,30,32,15)(8,26,17,28,18,29,27,12)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 6388);