Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C13×#2243 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
634 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4)(5,8)(6,7)(9,10)(11,12)(13,22)(14,19)(15,18)(16,24)(17,21)(20,23)(25,26);(4,7)(8,10)(11,12,15,19,16,20,22,26,17,21,25,13,23,24,14,18);(3,5,6,9)(4,8,7,10)(11,13,14,21,23,26,25,20,17,19,22,12,16,18,15,24)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26686);