Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13068 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1893 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
470 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)(14,15)(16,25)(17,30,33,41)(18,28)(19,23)(20,27)(21,24)(22,32,40,38)(26,31,39,34)(29,35)(36,37)(42,43,45,44);(14,16,25,15,20,28,36,23,21,29,35,24,19,37,18,27)(17,26,42,22,32,44,31,41,33,39,45,40,38,43,34,30);(14,17)(15,22)(16,26)(18,34)(19,38)(20,32)(21,33)(23,41)(24,40)(25,42)(27,30)(28,44)(29,39)(31,36)(35,45)(37,43)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6056);