Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
820 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)(14,15,18,23,19,24,34,22)(16,25,28,20,30,26,29,36)(17,31,32,21,33,37,45,38)(27,41,42,39,44,35,43,40);(14,16,18,28,19,30,34,29)(15,20,22,25,24,36,23,26)(17,27,32,42,33,44,45,43)(21,35,31,39,38,41,37,40);(14,15)(16,26)(17,21)(18,22)(19,24)(20,28)(23,34)(25,30)(27,40)(29,36)(31,32)(33,38)(35,42)(37,45)(39,44)(41,43);(14,17,18,32,19,33,34,45)(15,21,22,31,24,38,23,37)(16,27,28,42,30,44,29,43)(20,35,25,39,36,41,26,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17796);