Finite Group DatabasebetaFinite Group Databasebeta| order | 1624 |
| isoclinism | isoclinic class of AGL(1,𝔽29) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽29) |
| unambiguous semidirect product | #1181⋊(C2×C7) |
| unambiguous semidirect product | (C2×#1181)⋊C7 |
| unambiguous semidirect product | (D29⋊C7)⋊C4 |
| Fitting, socle | C2×C29 ⋊ C4×C7 |
| derived, Sylow | C29 ⋊ C2×C4×C7 |
| Hall | C2×#1181 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽29) |
| commutator, hypocenter | C29 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29 | C4×C7 |
| prime radical | C2×D29⋊C7 | C2 |
| cosocle | D29 | C22×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 58 |
58 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1624, 43);