Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
958 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)(16,25,28,36,29,38,27,20)(17,30,32,37,33,39,31,21)(26,35,41,44,42,45,43,40);(14,16,18,28,19,29,34,27)(15,20,23,25,24,36,22,38)(17,26,32,41,33,42,31,43)(21,35,30,44,37,45,39,40);(14,17,19,33)(15,21,24,37)(16,26,29,42)(18,31,34,32)(20,35,36,45)(22,30,23,39)(25,40,38,44)(27,41,28,43);(14,15)(16,20)(17,21)(18,23)(19,24)(22,34)(25,28)(26,35)(27,38)(29,36)(30,32)(31,39)(33,37)(40,43)(41,44)(42,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18186);