Finite Group DatabasebetaFinite Group Databasebeta| order | 8442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×#13064105 |
| Fitting, socle | C2×C3×C7×C67 ⋊ C3 |
| derived, Hall | C7×C67 ⋊ C2×C32 |
| Hall | C2×C7×C67 ⋊ C32 |
| Hall | C2×C67 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C67 ⋊ C2×C3×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C3×C67⋊C3 |
| Sylow | C7 ⋊ C2×C3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #13064105 |
| commutator, hypocenter | C7×C67 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C67 | C3 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
954 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19150595, C3×#19150591, C3×#19150587, … |
| maximal normal subgroup of | C3×#19150595, C3×#19150591, C3×#19150587, … |
| maximal quotient of | C3×C4×#13064105, C22×C3×#13064105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8442, 61);