Finite Group DatabasebetaFinite Group Databasebeta| order | 7868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11765499⋊C7 |
| Fitting, socle, derived, Sylow | C281 ⋊ C4×C7 |
| Hall | C281⋊C7 ⋊ C4 |
| Hall | #11765499 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C281 | C4×C7 |
| LCS | G ▷ C281 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,2,281|a^2=c,d^a=d^53,d^b=d^249,d^c=d^28038 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11765499⋊C7, C3⋊(#11765499⋊C7) |
| maximal normal subgroup of | C3×#11765499⋊C7 |
| maximal quotient of | C3×#11765499⋊C7, C3⋊(#11765499⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7868, 8);