Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C3×C53 ⋊ C2×C13 |
| derived, Sylow | C53 ⋊ C22×C3×C13 |
| Hall | C3×C53⋊C13 ⋊ C22 |
| Hall | C53⋊C13 ⋊ C22×C3 |
| Hall | C2×C3×D53 ⋊ C13 |
| Hall | C2×D53 ⋊ C3×C13 |
| Hall | C3×C53 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D53⋊C13 |
| commutator, hypocenter | C53 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C53 | C2×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9×D53⋊C13, C3×D3×D53⋊C13, C2×C32×D53⋊C13, … |
| maximal normal subgroup of | C2×C9×D53⋊C13, C2×C32×D53⋊C13 |
| maximal quotient of | C2×C9×D53⋊C13, C3×D3×D53⋊C13, C2×C32×D53⋊C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 22);