Finite Group DatabasebetaFinite Group Databasebeta| order | 8648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D4×C47⋊C23 |
| Fitting, Hall | D4×C47 ⋊ C23 |
| Sylow | C47 ⋊ D4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C47⋊C23 |
| commutator, socle, cosocle | C2×C47 | C22×C23 |
| Fitting | D4×C47 | C23 |
| hypercenter | D4 | C47⋊C23 |
| hypocenter | C47 | D4×C23 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ D4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 188 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽47), S4×C47⋊C23 |
| maximal normal subgroup of | D4×AGL(1,𝔽47) |
Past the SmallGroups library coverage — no SmallGroups id.