Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1128 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)(14,15,19,23)(16,20,26,34)(17,21,27,35)(18,29,31,22)(24,37,30,32)(25,39,40,33)(28,42,41,36)(38,44,43,45);(16,24,26,30)(20,32,34,37)(25,38,40,43)(33,44,39,45);(14,16)(15,20)(17,25)(18,30)(19,26)(21,33)(22,37)(23,34)(24,31)(27,40)(28,43)(29,32)(35,39)(36,45)(38,41)(42,44);(14,17)(15,21)(16,25)(18,28)(19,27)(20,33)(22,36)(23,35)(24,38)(26,40)(29,42)(30,43)(31,41)(32,44)(34,39)(37,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16980);