Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13158 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1936 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
316 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)(14,15,20,25,22,26,21,36)(16,18,24,37,29,27,39,19)(17,30,34,45,35,31,40,28)(23,41,42,33,44,32,43,38);(14,16,27,25,21,24,37,26,22,29,18,36,20,39,19,15)(17,31,32,23,34,45,38,43,35,30,41,44,40,28,33,42);(14,17,18,32,21,34,19,38,22,35,27,41,20,40,37,33)(15,23,16,28,25,43,24,31,26,44,29,45,36,42,39,30)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6146);