Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13391 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2033 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,27)(17,31)(18,33)(19,35)(20,24)(21,26)(22,28)(23,32)(25,34)(29,39)(30,40)(36,38)(37,41)(42,45)(43,44);(14,16)(15,22)(17,18)(19,29)(20,28)(21,30)(23,41)(24,40)(25,39)(26,31)(27,33)(32,34)(35,43)(36,44)(37,45)(38,42);(14,17,18,16,21,28,20,30)(15,23,24,42,26,43,33,39)(19,29,34,44,37,45,36,32)(22,38,27,41,31,25,40,35)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6379);