Finite Group DatabasebetaFinite Group Databasebeta| order | 8271 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C919 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C919⋊C3 |
| commutator, hypocenter | C919 | C9 |
| Fitting, socle | C3×C919 | C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,919|a^3=b,c^a=c^866927 conjugacy classes — view the full character table.
| maximal subgroup of | #22552000⋊C2, C2×#22552000, C9×C919⋊C3, … |
| maximal normal subgroup of | #22552000⋊C2, C2×#22552000, C9×C919⋊C3, … |
| maximal quotient of | C2×#22552000, #37613822, C3×#22552000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8271, 1);