Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of #1113⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#1113⋊C3 |
| unambiguous semidirect product | (C2×#1113)⋊C3 |
| Fitting, socle | C2×C33 ⋊ A4 |
| derived | #1113 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #1113⋊C3 |
| commutator, cosocle, hypocenter | #1113 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | A4 |
| LCS | G ▷ #1113 | |
| UCS | C1 ◁ C2 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18 |
26 conjugacy classes — view the full character table.
| maximal subgroup of | #13049365, #13049368, #88949⋊C3, … |
| maximal normal subgroup of | #13049365, #13049368, #88949⋊C3, … |
| maximal quotient of | #89042⋊C3, C4×#1113⋊C3, C2×SL(2,ℤ/9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 706);