Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23876 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24148 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,18)(19,21)(22,23)(24,30)(25,28)(26,35)(27,32)(29,34)(31,36)(33,37);(15,18)(19,20)(22,24)(23,27)(25,32)(26,31)(28,30)(29,36)(33,34)(35,37);(24,31)(26,34)(27,36)(29,35)(30,37)(32,33);(14,16,17,21)(15,19,18,20)(23,28)(27,30)(29,35)(36,37)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17136);