Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C2×D3×H(7,𝔽2) |
| Fitting | C2×C3×H(7,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C22×H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C26×D3 |
| commutator, cosocle | C2×C3 | C28 |
| Frattini | C2 | C27×D3 |
| Fitting | C2×C3×H(7,𝔽2) | C2 |
| socle | C22×C3 | C27 |
| hypercenter | C2×H(7,𝔽2) | D3 |
| hypocenter | C3 | C22×H(7,𝔽2) |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×H(7,𝔽2) | |
Only the 446425 normal subgroups are shown; non-normal subgroups are omitted.
390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#60399, D3×#6628896 |
| maximal normal subgroup of | C2×D3×#60399, D3×#6628896 |
Past the SmallGroups library coverage — no SmallGroups id.