Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2615 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C13×#41 ◁ G | |
1444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
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)(16,17)(22,23,28,34,27,25,26,30)(24,29,35,37,32,31,33,36);(15,17)(18,19)(20,21)(22,24)(23,29)(25,31)(26,33)(27,32)(28,35)(30,36)(34,37);(19,21)(22,25,27,23)(24,31,32,29)(26,30,28,34)(33,36,35,37);(15,17)(24,32)(29,31)(33,35)(36,37)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17384);