Finite Group DatabasebetaFinite Group Databasebeta| order | 7329 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C349 ⋊ C3 |
| Sylow | C349 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C349⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C349 | C3 |
| LCS | G ▷ C7×C349 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,349|b^a=b^2,c^a=c^122817 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20301080, #28412579, #28412583, … |
| maximal normal subgroup of | C2×#20301080, #28412579, #28412583, … |
| maximal quotient of | C2×#20301080, #36347109, C3×#20301080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7329, 3);