Finite Group DatabasebetaFinite Group Databasebeta| order | 5913 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×C9×C73 ⋊ C3 |
| Sylow | C73 ⋊ #731 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊(C73⋊C3) |
| commutator | C32×C73 | C32 |
| Frattini | C32 | C3×C73⋊C3 |
| Fitting | C3×C9×C73 | C3 |
| socle | C3×C73 | H(3,𝔽3) |
| hypercenter | C3×C9 | C73⋊C3 |
| hypocenter | C73 | #731 |
| LCS | G ▷ C32×C73 ▷ C3×C73 ▷ C73 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ C3×C9 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,73|b^3=d,b^a=bc,c^a=cd,e^a=e^8665 conjugacy classes — view the full character table.
| maximal subgroup of | #731×C73⋊C3, C3×#20238271, #31801407, … |
| maximal normal subgroup of | #731×C73⋊C3, C3×#20238271, #31801407, … |
| maximal quotient of | #31801221, #31801223, #31801225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5913, 32);