Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#106 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
636 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)(15,20,22,31)(17,27)(18,29)(21,30,33,41)(23,36,35,32)(25,39)(26,38)(28,40)(34,44,43,42)(37,45);(14,15,17,20,18,23,27,32,19,22,28,31,29,35,40,36)(16,21,25,30,26,34,39,42,24,33,37,41,38,43,45,44);(14,16)(15,21)(17,25)(18,26)(19,24)(20,30)(22,33)(23,34)(27,39)(28,37)(29,38)(31,41)(32,42)(35,43)(36,44)(40,45);(16,24)(21,33)(25,37)(26,38)(30,41)(34,43)(39,45)(42,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26392);