Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
| direct product | D3×#85496 |
| Fitting | C23×C3×D4 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×S4 |
| commutator, cosocle | C22×C3×A4 | C24 |
| Fitting | C23×C3×D4 | C2×D3 |
| socle | C24×C3 | C23×D3 |
| hypercenter | C2×D4 | D3×S4 |
| hypocenter | C3×A4 | C2×#127 |
| LCS | G ▷ C22×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
7166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11714540 |
| maximal normal subgroup of | D3×#11714540 |
Past the SmallGroups library coverage — no SmallGroups id.