Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D7×#64314 |
| Fitting | C32×C7×D4 ⋊ C23 |
| Hall | C32×C7 ⋊ C2×H(5,𝔽2) |
| Sylow | C32 ⋊ D7×H(5,𝔽2) |
| Sylow | C7 ⋊ C2×#64314 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D32×D7 |
| commutator, socle, cosocle | C2×C32×C7 | C25 |
| Fitting | C32×C7×D4 | C23 |
| hypercenter | D4 | D32×D7 |
| hypocenter | C32×C7 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 ◁ D4 | |
3828 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#10596675 |
| maximal normal subgroup of | D7×#10596675 |
Past the SmallGroups library coverage — no SmallGroups id.