Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C172) |
| derived, Sylow | C7 ⋊ C4×C172 |
| Hall | C7×C172 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C172 | D7 |
| commutator, hypocenter | C7 | C4×C172 |
| Frattini | C2 | D7×C172 |
| Fitting, socle | C2×C7×C172 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C172 | |
120 conjugacy classes of subgroups.
2890 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C172×ΓL(1,𝔽8)⋊C4, Dic7⋊(C172⋊C3), Dic7×C172⋊C3, … |
| maximal normal subgroup of | C172×ΓL(1,𝔽8)⋊C4, Dic7⋊(C172⋊C3), Dic7×C172⋊C3, … |
| maximal quotient of | C172×Dic21, C3×C172×Dic7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 15);