Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C199 ⋊ C3 |
| Sylow | C199 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C199⋊C3 |
| commutator, socle | C3×C199 | C32 |
| Fitting | C9×C199 | C3 |
| hypercenter | C9 | C199⋊C3 |
| hypocenter | C199 | 3−1+2 |
| LCS | G ▷ C3×C199 ▷ C199 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,199|a^3=c,b^a=bc,d^b=d^92605 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×C199⋊C3, C3×#19129016, #30633152, … |
| maximal normal subgroup of | 3−1+2×C199⋊C3, C3×#19129016, #30633152, … |
| maximal quotient of | #30633123, #30633125, #30633126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 11);