Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×C3⋊#85645 |
| Fitting | C27×C3 ⋊ C2×C3 |
| derived | C26×C3 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#85645 |
| commutator, cosocle, hypocenter | C26×C3 | C22×C3 |
| Frattini | C22 | C2×D3×C22⋊A4 |
| Fitting | C27×C3 | C2×C3 |
| socle | C25×C3 | C2×A4 |
| LCS | G ▷ C26×C3 | |
| UCS | C1 ◁ C2 | |
14682 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 14682 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231611, C2×D3×#85645 |
| maximal normal subgroup of | C2×#72231611, C2×D3×#85645 |
| maximal quotient of | C2×#72230753 |
Past the SmallGroups library coverage — no SmallGroups id.