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×#26405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,19,17,21)(22,23,28,32)(24,34,30,36)(25,35,26,29)(27,33,37,31);(14,16,18,17)(15,19,20,21)(22,24)(23,26)(25,32)(27,29)(28,30)(31,36)(33,34)(35,37);(14,17,18,16)(15,19,20,21)(22,25,28,26)(23,29,32,35)(24,33,30,31)(27,36,37,34);(22,26,28,25)(23,30,32,24)(27,36,37,34)(29,31,35,33)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19393);