Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C53×#60586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C53×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×#117×C53 ◁ G | |
2024 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,15)(12,17)(13,16)(14,19)(18,25)(20,27)(21,26)(22,29)(23,31)(24,30)(28,35)(32,36)(33,38)(34,37)(39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,8)(9,11,14,22)(10,15,19,29)(12,20,23,33)(13,21,25,35)(16,26,18,28)(17,27,31,38)(24,34,36,40)(30,37,32,39);(10,16)(13,25)(15,26)(17,30)(18,19)(21,35)(24,36)(27,37)(28,29)(31,32)(34,40)(38,39);(1,3,4,7)(2,6,5,8)(12,23)(17,31)(20,33)(24,36)(27,38)(30,32)(34,40)(37,39);(9,12,14,23)(10,17,19,31)(11,20,22,33)(13,24,25,36)(15,27,29,38)(16,30,18,32)(21,34,35,40)(26,37,28,39)3233 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53574);