Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D9×Dic9 |
| unambiguous semidirect product | (C9×D9)⋊C4 |
| derived, Sylow | C92 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D92 |
| commutator, hypocenter | C92 | C2×C4 |
| Frattini, socle | C2×C32 | D32 |
| Fitting, cosocle | C2×C92 | C22 |
| prime radical | C2×C3×D9 | D3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
93 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D9×Dic18, #13047074, #13047075, … |
| maximal normal subgroup of | D9×Dic18, #13047074, #13047075, … |
| maximal quotient of | D9×C9⋊C8, #13046362, Dic92, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 46);