Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#64314 |
| Fitting | C32×C7×D4 ⋊ C22 |
| Hall | C32×C7 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ C7×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7 | C22×D32 |
| commutator, cosocle | C2×C32 | C24×C7 |
| Frattini | C2 | C22×D32×C7 |
| Fitting | C32×C7×D4 | C22 |
| socle | C2×C32×C7 | C24 |
| hypercenter | C7×D4 | D32 |
| hypocenter | C32 | C7×H(5,𝔽2) |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C7 ◁ C7×D4 | |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#10596675, D7×#64314, #72246761, … |
| maximal normal subgroup of | C7×#10596675, D7×#64314, #72246761, … |
Past the SmallGroups library coverage — no SmallGroups id.