Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
1158 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)(16,24)(17,21)(18,22)(19,23)(20,27)(25,37)(26,38)(28,34)(29,35)(30,43)(31,36)(32,39)(33,41)(40,45)(42,44);(14,16,19,26)(15,20,23,33)(17,25,28,40)(18,27,31,41)(21,32,34,44)(22,24,36,38)(29,39,30,42)(35,37,43,45);(14,17)(15,21)(16,25)(18,30)(19,28)(20,32)(22,35)(23,34)(24,37)(26,40)(27,42)(29,31)(33,44)(36,43)(38,45)(39,41);(16,26)(17,28)(20,33)(21,34)(24,38)(27,41)(29,30)(35,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26546);