Finite Group DatabasebetaFinite Group Databasebeta| order | 812 |
| isoclinism | isoclinic class of D29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic29⋊C7 |
| derived, Sylow | C29 ⋊ C4×C7 |
| Hall | C29⋊C7 ⋊ C4 |
| Hall | Dic29 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D29⋊C7 |
| commutator, hypocenter | C29 | C4×C7 |
| Fitting, socle, cosocle | C2×C29 | C2×C7 |
| prime radical | C2×C29⋊C7 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 116 |
Polycyclic presentation:
2,7,2,29|a^2=c,d^a=d^28,d^b=d^1632 conjugacy classes — view the full character table.
| maximal subgroup of | #6599⋊C7, (C29⋊C7)⋊Q8, C4×D29⋊C7, … |
| maximal normal subgroup of | #6599⋊C7, (C29⋊C7)⋊Q8, C4×D29⋊C7, … |
| maximal quotient of | #6597⋊C7, C2×Dic29⋊C7, C3×Dic29⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(812, 1);