Finite Group DatabasebetaFinite Group Databasebeta| order | 7347 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C79 ⋊ C3 |
| Sylow | C79 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C79 | C3 |
| LCS | G ▷ C31×C79 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,31,79|b^a=b^25,c^a=c^23819 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20301166, #28412806, #28412810, … |
| maximal normal subgroup of | C2×#20301166, #28412806, #28412810, … |
| maximal quotient of | C2×#20301166, #36347521, C3×#20301166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7347, 4);