Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C13×#1673 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(4,7)(5,8)(9,10)(11,12,14,17)(13,15,18,16);(3,4,8,10,6,9,5,7);(12,15)(13,18)(16,17)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12091);