Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C4×C7 |
| direct product | #127×#3862 |
| Fitting, Hall | C72×#127 ⋊ C3 |
| Sylow | C72 ⋊ C3×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3862 |
| commutator, socle, cosocle | C22×C72 | C23×C3 |
| Fitting | C72×#127 | C3 |
| hypercenter | #127 | #3862 |
| hypocenter | C72 | C3×#127 |
| LCS | G ▷ C22×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ #127 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
266 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #127×#64425, ΓL(1,𝔽8)2×#127, #72246049, … |
| maximal normal subgroup of | #127×#64425, ΓL(1,𝔽8)2×#127, #72246049, … |
Past the SmallGroups library coverage — no SmallGroups id.