Finite Group DatabasebetaFinite Group Databasebeta| order | 1967 |
| isoclinism | isoclinic class of C281⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C281⋊C7 |
| Fitting, socle, derived, Sylow | C281 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C281 | C7 |
| LCS | G ▷ C281 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 281 |
| transitive degree | μt(G) = 281 |
Polycyclic presentation:
7,281|b^a=b^24947 conjugacy classes — view the full character table.
| maximal subgroup of | D281⋊C7, C2×C281⋊C7, C7×C281⋊C7, … |
| maximal normal subgroup of | D281⋊C7, C2×C281⋊C7, C7×C281⋊C7, … |
| maximal quotient of | C2×C281⋊C7, C281⋊C49, C7×C281⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1967, 1);