Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #31077 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32703 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | #2782 |
| prime radical | C13×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23,20,25,18,24)(16,26,29,21,30,37,28,38)(17,31,35,22,33,41,34,40)(27,42,43,39,44,36,32,45);(14,16)(15,21)(17,32)(18,28)(19,29)(20,30)(22,39)(23,37)(24,26)(25,38)(27,35)(31,42)(33,43)(34,44)(36,41)(40,45);(14,17,18,34,20,33,19,35)(15,22,23,41,25,40,24,31)(16,27,29,43,30,44,28,32)(21,36,26,39,38,42,37,45);(16,28,30,29)(17,33)(21,37,38,26)(22,40)(27,43,44,32)(31,41)(34,35)(36,39,42,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25691);