Finite Group DatabasebetaFinite Group Databasebeta| order | 10053 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1117 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1117 | C9 |
| prime radical, cosocle | C1117⋊C3 | C3 |
| LCS | G ▷ C1117 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,1117|a^3=b,c^a=c^529,c^b=c^996133 conjugacy classes — view the full character table.
| maximal subgroup of | #23758409⋊C2, C2×#23758409, C3×#23758409 |
| maximal normal subgroup of | #23758409⋊C2, C2×#23758409, C3×#23758409 |
| maximal quotient of | C2×#23758409, #44474785, C3×#23758409 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10053, 3);