Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C199⋊C3) |
| unambiguous semidirect product | C199⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C199⋊C3)⋊C3 |
| Fitting | C32×C199 ⋊ C3 |
| Sylow | C199 ⋊ H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C199⋊C3 |
| commutator, socle | C3×C199 | C32 |
| Fitting | C32×C199 | C3 |
| hypercenter | C32 | C199⋊C3 |
| hypocenter | C199 | H(3,𝔽3) |
| LCS | G ▷ C3×C199 ▷ C199 | |
| UCS | C1 ◁ C3 ◁ C32 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,199|b^a=bc,d^b=d^106605 conjugacy classes — view the full character table.
| maximal subgroup of | #30633134, #30633135, #30633137, … |
| maximal normal subgroup of | #30633134, #30633135, #30633137, … |
| maximal quotient of | #30633123, C32⋊#13184224, #30633133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 9);