Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13323 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
534 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)(15,21)(16,26)(17,30)(18,19)(22,39)(23,37)(24,31)(25,38)(27,40)(28,32)(29,35)(33,34)(36,41)(42,45);(14,15)(16,27)(17,31)(18,23)(19,24)(20,25)(21,30)(22,26)(28,36)(29,41)(32,40)(33,38)(34,37)(35,42)(39,43)(44,45);(14,16)(15,22)(17,32)(18,35)(19,26)(20,29)(21,36)(23,27)(24,41)(25,42)(28,34)(30,44)(31,45)(33,43)(37,39)(38,40)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6311);