Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#32697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×#41×C53 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2,7,11,6,12,24,32)(3,8,16,27,15,18,25,31)(4,17,20,14,19,9,28,21)(5,10,23,29,22,30,26,13)(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)(2,8)(4,10)(5,21)(6,15)(7,25)(9,23)(11,31)(12,18)(13,20)(14,22)(16,24)(17,26)(19,30)(27,32)(28,29);(1,4,6,19)(2,9)(3,13)(5,18,22,8)(7,20,24,28)(10,16)(11,21)(12,17)(14,32)(15,29)(23,31,26,27)(25,30);(1,5,6,22)(2,10,12,30)(3,14,15,21)(4,18,19,8)(7,26,24,23)(9,16,17,25)(11,13,32,29)(20,27,28,31)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 25685);