Finite Group DatabasebetaFinite Group Databasebeta| order | 5913 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#10620323 |
| commutator, socle | C3×C73 | C3×C9 |
| Fitting | C32×C73 | C9 |
| hypercenter | C32 | #10620323 |
| hypocenter | C73 | C27⋊C3 |
| LCS | G ▷ C3×C73 ▷ C73 | |
| UCS | C1 ◁ C3 ◁ C32 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,73|a^3=c,c^3=d,b^a=bd,e^a=e^2,e^c=e^8105 conjugacy classes — view the full character table.
| maximal subgroup of | #31801469, #31801470, #31801471, … |
| maximal normal subgroup of | #31801469, #31801470, #31801471, … |
| maximal quotient of | #31801463, C32⋊#14520299, #31801480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5913, 57);