Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2 |
| direct product | D72×C41 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C41) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×C41) |
| Fitting, socle, Hall | C72×C41 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D72 |
| commutator, hypocenter | C72 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C72×C41 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C41 | |
52 conjugacy classes of subgroups.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#64418⋊C2, D7×C41×AGL(1,𝔽7), C41×#64423⋊C2, … |
| maximal normal subgroup of | D7×C41×AGL(1,𝔽7), C41×#64423⋊C2, C41×#64422⋊C2, … |
| maximal quotient of | C3×D72×C41, D7×C41×D21, C41×D21⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 24);