Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#60726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3512 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×#41×C53 ◁ G | |
1842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,18)(11,19,20,34)(12,16,23,31)(13,26,27,17)(15,28,29,22)(21,35,24,38)(25,40,36,33)(30,39,32,37)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,8)(11,20)(12,23)(15,29)(16,31)(19,34)(22,28)(25,36)(33,40);(9,11,13,22,14,20,27,28)(10,15,17,19,18,29,26,34)(12,24,25,39,23,21,36,37)(16,32,33,38,31,30,40,35);(1,3,4,7)(2,6,5,8)(12,23)(16,31)(21,24)(25,36)(30,32)(33,40)(35,38)(37,39);(9,12)(10,16)(11,21)(13,25)(14,23)(15,30)(17,33)(18,31)(19,35)(20,24)(22,37)(26,40)(27,36)(28,39)(29,32)(34,38)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53714);