Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,18)(16,20,21,19)(22,23,26,31,27,32,42,29)(24,33,36,44,37,47,34,28)(25,38,39,46,41,45,40,30)(35,43,49,52,51,53,50,48);(15,18)(19,20)(22,24,27,37)(23,28,32,44)(25,35,41,51)(26,34,42,36)(29,33,31,47)(30,43,46,53)(38,48,45,52)(39,50,40,49);(23,29)(24,34)(26,42)(30,38)(31,32)(33,47)(35,49)(36,37)(39,40)(45,46)(48,52)(50,51);(14,16,17,21)(15,19,18,20)(22,25,27,41)(23,30,32,46)(24,35,37,51)(26,40,42,39)(28,43,44,53)(29,38,31,45)(33,48,47,52)(34,49,36,50)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19910);