Finite Group DatabasebetaFinite Group Databasebeta| order | 812 |
| isoclinism | isoclinic class of D7×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D29 |
| unambiguous semidirect product | (D7×C29)⋊C2 |
| unambiguous semidirect product | (C7×D29)⋊C2 |
| unambiguous semidirect product | D203⋊C2 |
| Fitting, socle, derived, Hall | C7×C29 ⋊ C22 |
| Sylow | C29 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C29 | C22 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 203 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1181, C2×D7×D29, AGL(1,𝔽7)×D29, … |
| maximal normal subgroup of | D7×#1181, C2×D7×D29, AGL(1,𝔽7)×D29, … |
| maximal quotient of | Dic7×D29, D7×Dic29, #13108596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(812, 12);