Finite Group DatabasebetaFinite Group Databasebeta| order | 6388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1597 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1597 | C4 |
| LCS | G ▷ C1597 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1597|a^2=b,c^a=c^610,c^b=c^1596403 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20264116, #20264116⋊C3, C3×#20264116, … |
| maximal normal subgroup of | C2×#20264116, #20264116⋊C3, C3×#20264116, … |
| maximal quotient of | #27165159, C2×#20264116, C3×#20264116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6388, 3);