Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#548 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,27,32,35)(28,30,34,31)(29,37,41,36)(33,39,38,40);(19,22)(23,25)(26,28)(27,30)(29,38)(31,35)(32,34)(33,41)(36,39)(37,40);(15,17)(18,20,21,24)(19,23,22,25)(26,29)(27,33)(28,36)(30,39)(31,40)(32,41)(34,37)(35,38);(19,22)(23,25)(26,30,32,31)(27,34,35,28)(29,39,41,40)(33,37,38,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17028);