Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C17 |
| direct product | C7×#11923880 |
| derived, Sylow | C172 ⋊ C4×C7 |
| Hall | C7×C172 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C17⋊D17 |
| commutator, hypocenter | C172 | C4×C7 |
| Frattini | C2 | C7×C17⋊D17 |
| Fitting, socle | C2×C7×C172 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2×C7 | |
120 conjugacy classes of subgroups.
2044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 14);