Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13229 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1964 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
452 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)(16,26,30,41)(17,31)(18,34,27,23)(19,37)(20,25)(21,22)(24,38)(28,42,43,36)(29,32,44,40)(33,45)(35,39);(14,16,27,22,20,30,18,35)(15,21,34,41,25,39,23,26)(17,28,40,24,33,43,32,37)(19,29,42,31,38,44,36,45);(14,17,19,21,20,33,38,39)(15,22,24,31,25,35,37,45)(16,28,29,34,30,43,44,23)(18,32,36,26,27,40,42,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6217);