Finite Group DatabasebetaFinite Group Databasebeta| order | 5913 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | C73⋊C3 |
| commutator, hypocenter | C73 | C81 |
| Fitting | C27×C73 | C3 |
| socle | C3×C73 | C27 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C27 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,73|a^3=b,b^3=c,c^3=d,e^a=e^8729 conjugacy classes — view the full character table.
| maximal subgroup of | C81×C73⋊C3, C3×#20238255, #31801273, … |
| maximal normal subgroup of | C81×C73⋊C3, C3×#20238255, #31801273, … |
| maximal quotient of | #31801215, C3×#20238255 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5913, 16);