Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13197 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #121 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1954 |
| prime radical | C2×C13×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
424 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)(14,15,19,26,20,25,36,41,21,27,35,23,18,24,17,34)(16,28,32,44,30,40,29,43,33,42,37,45,31,22,38,39);(14,16,17,29,18,31,35,32,21,33,36,38,20,30,19,37)(15,22,34,44,24,42,23,39,27,40,41,45,25,28,26,43);(14,17,18,35,21,36,20,19)(15,23,25,34,27,26,24,41)(16,29,31,32,33,38,30,37)(22,39,28,44,40,43,42,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6185);