Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#19051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C53 |
| prime radical | C53×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(2,5)(3,7)(6,8)(9,10,14,18)(11,19,22,33)(12,16,23,31)(13,25,28,17)(15,26,30,21)(20,36,37,35)(24,34,27,32)(29,39,40,38)(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);(3,7)(5,8)(9,11)(10,15)(12,20)(13,26)(14,22)(16,29)(17,33)(18,30)(19,25)(21,28)(23,37)(24,39)(27,38)(31,40)(32,35)(34,36);(1,2)(3,8)(4,6)(5,7)(9,12)(10,16)(11,20)(13,27)(14,23)(15,29)(17,34)(18,31)(19,35)(21,39)(22,37)(24,28)(25,32)(26,38)(30,40)(33,36);(12,23)(16,31)(20,37)(24,27)(29,40)(32,34)(35,36)(38,39)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 12039);