Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×C3×#35346⋊C3 |
| Fitting | C2×C3×#35346 ⋊ C3 |
| derived | C22×H(5,𝔽2) ⋊ C22×C32 |
| Sylow | C2×#35346 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #85645 |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C22×C32 |
| Frattini | C23 | C22×C3×C22⋊A4 |
| Fitting | C2×C3×#35346 | C3 |
| socle | C24×C3 | C2×C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C22×C3 | |
23516 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 23516 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72209653, C2×D3×#35346⋊C3, C2×#72231672 |
| maximal normal subgroup of | C2×C3×#72209653, C2×D3×#35346⋊C3, C2×#72231672 |
| maximal quotient of | C2×C3×#72209831 |
Past the SmallGroups library coverage — no SmallGroups id.