Finite Group DatabasebetaFinite Group Databasebeta| order | 4887 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C181 ⋊ C3 |
| Sylow | C181 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C181⋊C3 |
| commutator, socle | C3×C181 | C32 |
| Fitting | C9×C181 | C3 |
| hypercenter | C9 | C181⋊C3 |
| hypocenter | C181 | 3−1+2 |
| LCS | G ▷ C3×C181 ▷ C181 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,181|a^3=c,b^a=bc,d^b=d^48551 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×C181⋊C3, C3×#19096560, #28412650, … |
| maximal normal subgroup of | 3−1+2×C181⋊C3, C3×#19096560, #28412650, … |
| maximal quotient of | #28412621, #28412623, #28412625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4887, 10);