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×#33897 |
| 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×D4×C13 ◁ C8×D4×C13 ◁ G | |
580 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)(14,15,17,19)(16,20,21,18)(23,28)(24,26)(25,32)(29,36)(30,37)(31,34)(33,35);(14,16)(15,18)(17,21)(19,20)(23,29)(28,36)(30,35)(33,37);(22,23)(24,30)(25,33)(26,35)(27,29)(28,32)(31,36)(34,37);(16,21)(18,20)(22,24,27,26)(23,30,29,35)(25,31,34,32)(28,33,36,37)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26885);