Finite Group DatabasebetaFinite Group Databasebeta| order | 7868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic281⋊C7 |
| derived, Sylow | C281 ⋊ C4×C7 |
| Hall | C281⋊C7 ⋊ C4 |
| Hall | Dic281 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D281⋊C7 |
| commutator, hypocenter | C281 | C4×C7 |
| Fitting, socle | C2×C281 | C2×C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,281,2|a^2=d,c^a=c^280,c^b=c^24968 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic281⋊C7, C3⋊(Dic281⋊C7) |
| maximal normal subgroup of | C3×Dic281⋊C7 |
| maximal quotient of | C3×Dic281⋊C7, C3⋊(Dic281⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7868, 2);