Finite Group DatabasebetaFinite Group Databasebeta| order | 812 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | Dic7×C29 |
| unambiguous semidirect product | C7⋊(C4×C29) |
| derived, Sylow | C7 ⋊ C4×C29 |
| Hall | C7×C29 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D7 |
| commutator, hypocenter | C7 | C4×C29 |
| Frattini | C2 | D7×C29 |
| Fitting, socle, prime radical | C2×C7×C29 | C2 |
| cosocle | C2×C7 | C2×C29 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 812 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7×D29, #13108596, #13108598, … |
| maximal normal subgroup of | Dic7×D29, #13108596, #13108598, … |
| maximal quotient of | C29×C7⋊C8, C2×Dic7×C29, C3×Dic7×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(812, 3);