Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×C3⋊D32 |
| Fitting, socle | C2×C34 ⋊ C22 |
| derived, Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D32 |
| commutator, cosocle, hypocenter | C34 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #13049396, #13049403, #13049410, … |
| maximal normal subgroup of | #13049396, #13049403, #13049410, … |
| maximal quotient of | C3⋊D3×#634, #13049687, #13049688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 750);