Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C199 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C199⋊C3 |
| commutator, hypocenter | C199 | C27 |
| Fitting | C9×C199 | C3 |
| socle | C3×C199 | C9 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,199|a^3=b,b^3=c,d^a=d^106621 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C199⋊C3, C3×#19129011, #30633130, … |
| maximal normal subgroup of | C27×C199⋊C3, C3×#19129011, #30633130, … |
| maximal quotient of | #30633121, C3×#19129011 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 6);