Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10811 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C2×C13 | #1434 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C13×M16 ◁ G | |
644 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26,29,36)(17,31)(18,23)(19,24)(20,25)(21,28,37,30)(22,33)(27,41,44,35)(32,38)(34,39)(40,42,45,43);(14,16,19,30,20,29,18,28)(15,21,23,26,25,37,24,36)(17,27,33,43,34,44,32,42)(22,35,31,40,38,41,39,45);(14,17,18,32,20,34,19,33)(15,22,23,31,25,38,24,39)(16,27,28,42,29,44,30,43)(21,35,26,40,37,41,36,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3799);