Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#22458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#576 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1338 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)(14,15,19,24,20,25,18,33)(16,26,29,21,30,39,34,38)(17,23,31,40,32,22,35,41)(27,43,28,36,45,37,44,42);(14,16)(15,21)(17,27)(18,34)(19,29)(20,30)(22,36)(23,42)(24,39)(25,38)(26,33)(28,31)(32,45)(35,44)(37,41)(40,43);(14,17)(15,22)(16,27)(18,31)(19,35)(20,32)(21,36)(23,25)(24,40)(26,37)(28,34)(29,44)(30,45)(33,41)(38,42)(39,43);(14,17)(15,23)(16,28)(18,35)(19,31)(20,32)(21,37)(22,25)(24,40)(26,36)(27,34)(29,45)(30,44)(33,41)(38,43)(39,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15446);