Finite Group DatabasebetaFinite Group Databasebeta| order | 854 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D61 |
| unambiguous semidirect product | C61⋊(C2×C7) |
| Fitting, socle, Hall | C7×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 427 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#6923, C7⋊#6923, D7×D61, … |
| maximal normal subgroup of | C7×#6923, C7⋊#6923, D7×D61, … |
| maximal quotient of | C7×Dic61, C2×C7×D61, C3×C7×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(854, 2);