Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of #87973 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#87975 |
| Hall | C32×C17 ⋊ D4 |
| Sylow | C17 ⋊ C3×D12 |
| Sylow | C32 ⋊ C22⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D17 |
| commutator, cosocle | C2×C3×C17 | C22×C3 |
| Frattini | C2 | C3×D3×D17 |
| Fitting, socle | C2×C32×C17 | C22 |
| hypocenter | C3×C17 | C3×D4 |
| LCS | G ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C2×C3 | |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 408 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 64);