Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C13×#1694 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(4,7)(5,8)(9,10)(11,12,15,18)(13,19,21,26)(14,22,24,17)(16,23,25,20);(3,4,8,10,6,9,5,7);(4,9)(7,10)(11,13,15,21)(12,16,18,25)(14,23,24,20)(17,26,22,19)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12136);