Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×#997 |
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2×C3 |
| derived | C3×H(5,𝔽2) ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×C22⋊A4 |
| commutator, cosocle, hypocenter | C3×H(5,𝔽2) | C23×C3 |
| Frattini | C2 | C22×D3×C22⋊A4 |
| Fitting | C22×C3×H(5,𝔽2) | C2×C3 |
| socle | C23×C3 | C2×C22⋊A4 |
| LCS | G ▷ C3×H(5,𝔽2) | |
| UCS | C1 ◁ C23 | |
23041 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 23041 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#5934, C2×D3×#11710730 |
| maximal normal subgroup of | C22×D3×#5934 |
| maximal quotient of | C2×D3×#35346⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.