Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
546 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)(16,25)(17,22)(18,31)(19,29)(20,24)(21,28)(23,34)(26,40)(27,42)(30,32)(33,39)(35,45)(36,43)(37,44)(38,41);(14,15)(16,21)(17,29)(18,32)(19,22)(20,24)(23,35)(25,41)(26,39)(27,38)(28,42)(30,31)(33,43)(34,45)(36,37)(40,44);(14,16,19,36,20,27,17,26)(15,21,22,37,24,38,29,39)(18,33,34,41,35,44,30,28)(23,40,31,42,32,43,45,25);(14,17,20,19)(15,22,24,29)(16,26,27,36)(18,30,35,34)(21,37,38,39)(23,31,32,45)(25,40,42,43)(28,44,41,33)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26647);