Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| 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 | |
1122 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)(16,21)(17,28)(18,23)(19,34)(20,25)(22,32)(24,37)(26,42)(27,33)(29,45)(30,44)(31,41)(35,39)(36,40)(38,43);(14,16,20,23)(15,21,25,18)(17,29)(19,27,37,40)(22,38)(24,36,34,33)(26,31)(28,42)(30,39)(32,44)(35,43)(41,45);(14,17)(15,22)(16,26)(18,30)(19,35)(20,31)(21,38)(23,29)(24,41)(25,39)(27,44)(28,34)(32,37)(33,42)(36,45)(40,43);(14,18,20,21)(15,23,25,16)(17,30,31,38)(19,36,37,33)(22,29,39,26)(24,27,34,40)(28,43,41,44)(32,42,35,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16989);