Finite Group DatabasebetaFinite Group Databasebeta| order | 612 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D17 |
| unambiguous semidirect product | C17⋊(C22×C32) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C32) |
| Fitting, socle | C2×C32×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C22×C32 |
| Hall | C32×C17 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D17 |
| commutator, cosocle, hypocenter | C17 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 306 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×D17, C3×#87973, C3×#87974, … |
| maximal normal subgroup of | C3×Dic3×D17, C3×#87973, C3×#87974, … |
| maximal quotient of | C32×Dic34, C32×C4×D17, C32×D68, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(612, 31);