Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19812 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C2×D4×C13 | C2×D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
616 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)(15,18)(16,21)(19,20)(22,23,26,29)(24,30,32,37)(25,33,35,28)(27,34,36,31);(14,15,17,20)(16,19,21,18);(22,24,26,32)(23,27,29,36)(25,34,35,31)(28,37,33,30);(15,19)(16,21)(18,20)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12800);