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 | C3 | #13184226 |
| commutator, hypocenter | C199 | C27 |
| Fitting, socle | C3×C199 | C9 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,199|a^3=b,b^3=c,d^a=d^175,d^b=d^10693 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19129019, (C199⋊C3)⋊C27, #30633162, … |
| maximal normal subgroup of | C3×#19129019, (C199⋊C3)⋊C27, #30633162, … |
| maximal quotient of | #30633155, C3×#19129019 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 14);