Finite Group DatabasebetaFinite Group Databasebeta| order | 8463 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C31 ⋊ C3 |
| Hall | C13×C31 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C31 ⋊ C13⋊C3 |
| Hall | C7×C13 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ #63271 |
| Sylow | C13 ⋊ #10620253 |
| Sylow | C7 ⋊ #11925881 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C31 | C3 |
| LCS | G ▷ C7×C13×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,13,31|b^a=b^2,c^a=c^9,d^a=d^25943 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22554956, #30683615, #30683628, … |
| maximal normal subgroup of | C2×#22554956, #30683615, #30683628, … |
| maximal quotient of | C2×#22554956, #38761835, C3×#22554956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8463, 13);