Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33964 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G | |
554 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)(15,19)(20,21)(23,27)(24,30)(25,32)(28,35)(29,36)(31,34)(33,37);(14,15,18,19)(16,20,17,21)(23,28)(27,35)(29,34)(31,36);(14,16,18,17)(15,20,19,21)(22,23)(24,31)(25,34)(26,28)(27,30)(29,32)(33,36)(35,37);(14,17,18,16)(15,20,19,21)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26952);