Finite Group DatabasebetaFinite Group Databasebeta| order | 1624 |
| isoclinism | isoclinic class of AGL(1,𝔽29) |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6599⋊C7 |
| derived, Sylow | C29 ⋊ C7×C8 |
| Hall | #6599 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽29) |
| commutator, hypocenter | C29 | C7×C8 |
| Fitting, socle | C2×C29 | C4×C7 |
| prime radical | C2×C29⋊C7 | C4 |
| cosocle | Dic29 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2,7,2^2,29|a^2=c,c^2=d,e^a=e^12,e^b=e^24,e^c=e^2858 conjugacy classes — view the full character table.
| maximal subgroup of | #72277014, #72277018, #72277024 |
| maximal normal subgroup of | #72277014, #72277018, #72277024 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1624, 7);