Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | AGL(1,𝔽7)×#3802 |
| Fitting | C32×C4×C7 ⋊ C23×C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C22×D4 |
| Sylow | C7 ⋊ C2×C3×#3802 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×AGL(1,𝔽7) |
| commutator, socle, cosocle | C2×C32×C7 | C24×C3 |
| Fitting | C32×C4×C7 | C23×C3 |
| hypercenter | C4 | D32×AGL(1,𝔽7) |
| hypocenter | C32×C7 | C22×C3×D4 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 ◁ C4 | |
2244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D4×AGL(1,𝔽7), AGL(1,𝔽7)×#64306, AGL(1,𝔽7)×#63926 |
| maximal normal subgroup of | D32×D4×AGL(1,𝔽7), AGL(1,𝔽7)×#64306, AGL(1,𝔽7)×#63926 |
Past the SmallGroups library coverage — no SmallGroups id.