Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D3×#41×S4 |
| Fitting | C22×C3×#41 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D3×S4 |
| commutator, cosocle | C2×C3×A4 | C25 |
| Frattini | C2 | C23×D3×S4 |
| Fitting | C22×C3×#41 | C2×D3 |
| socle | C23×C3 | C24×D3 |
| hypercenter | #41 | D3×S4 |
| hypocenter | C3×A4 | C22×#41 |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C4 ◁ #41 | |
12194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D3×S4×AGL(1,ℤ/8) |
| maximal normal subgroup of | D3×S4×AGL(1,ℤ/8) |
Past the SmallGroups library coverage — no SmallGroups id.