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×#26402 |
| 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)(22,23,27,31)(24,33,29,36)(25,34,35,28)(26,32,37,30);(14,16,18,17)(15,19,20,21)(22,24,27,29)(23,25,31,35)(26,34,37,28)(30,36,32,33);(14,17,18,16)(15,19,20,21)(22,25)(23,28)(24,32)(26,33)(27,35)(29,30)(31,34)(36,37);(22,25)(23,29)(24,31)(26,36)(27,35)(28,30)(32,34)(33,37)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19390);