Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C33 |
| direct product | C3×(2−1+4⋊C3)⋊A4 |
| Fitting | C3×H(7,𝔽2) ⋊ C32 |
| Sylow | H(7,𝔽2) ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C22×A42 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C22×C33 |
| Frattini | C2 | C22×C3×A42 |
| Fitting | C3×H(7,𝔽2) | C32 |
| hypercenter | C3×D4 | A42 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
1806 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
219 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72224794 |
| maximal normal subgroup of | C3×#72224794 |
| maximal quotient of | #72245618 |
Past the SmallGroups library coverage — no SmallGroups id.