Finite Group DatabasebetaFinite Group Databasebeta| order | 9436 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C337 · Schur multiplier (H2) = C1 |
| direct product | Dic7×C337 |
| unambiguous semidirect product | C7⋊(C4×C337) |
| derived, Sylow | C7 ⋊ C4×C337 |
| Hall | C7×C337 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C337 | D7 |
| commutator, hypocenter | C7 | C4×C337 |
| Frattini | C2 | D7×C337 |
| Fitting, socle | C2×C7×C337 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C337 | |
12 conjugacy classes of subgroups.
3370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic7×C337, Dic21×C337, Dic7×C337⋊C3, … |
| maximal normal subgroup of | C3×Dic7×C337, Dic7×C337⋊C3, ΓL(1,𝔽8)⋊C4×C337, … |
| maximal quotient of | C3×Dic7×C337, Dic21×C337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9436, 4);