Finite Group DatabasebetaFinite Group Databasebeta| order | 8034 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#16860815 |
| Fitting, socle, Hall | C2×C13×C103 ⋊ C3 |
| derived, Hall | C13×C103 ⋊ C2×C3 |
| Hall | C2×C103 ⋊ C13⋊C3 |
| Sylow | C103 ⋊ C2×C13⋊C3 |
| Hall | C2×C13 ⋊ C103⋊C3 |
| Sylow | C13 ⋊ C2×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16860815 |
| commutator, hypocenter | C13×C103 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C103 | C3 |
| LCS | G ▷ C13×C103 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
898 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16860815, #30632546, #30632550, … |
| maximal normal subgroup of | C4×#16860815, #30632546, #30632550, … |
| maximal quotient of | C4×#16860815, C22×#16860815, C2×#27130261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8034, 5);