Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13247 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1972 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
414 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)(14,15,20,25)(16,18,24,36)(17,29)(19,38,37,23)(21,28,35,26)(22,39)(27,34)(30,33)(31,40)(32,41)(42,43)(44,45);(14,16,19,26,21,23,18,25,20,24,37,28,35,38,36,15)(17,30,39,22,33,29,43,40,34,44,32,41,45,27,31,42);(14,17,19,32,21,33,18,31,20,34,37,39,35,45,36,43)(15,22,24,29,26,40,38,44,25,41,16,27,28,42,23,30)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6235);