Finite Group DatabasebetaFinite Group Databasebeta| order | 8148 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C97⋊C3 |
| Fitting, socle | C2×C7×C97 ⋊ C2×C3 |
| derived, Hall | C7×C97 ⋊ C22×C3 |
| Hall | C2×D7×C97 ⋊ C3 |
| Hall | C7×C97⋊C3 ⋊ C22 |
| Sylow | C97 ⋊ C2×C3×D7 |
| Sylow | C7 ⋊ C22×C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×C97⋊C3 |
| commutator, hypocenter | C7×C97 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C97 | C2×C3 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)×C97⋊C3, D3×D7×C97⋊C3, C2×C3×D7×C97⋊C3, … |
| maximal normal subgroup of | C2×AGL(1,𝔽7)×C97⋊C3, C2×C3×D7×C97⋊C3 |
| maximal quotient of | C2×D7×C97⋊C9, D3×D7×C97⋊C3, C2×C3×D7×C97⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8148, 49);