Finite Group DatabasebetaFinite Group Databasebeta| order | 18477 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2053 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2053 | C9 |
| prime radical, cosocle | C2053⋊C3 | C3 |
| LCS | G ▷ C2053 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2053 |
Polycyclic presentation:
3^2,2053|a^3=b,c^a=c^215,c^b=c^1855237 conjugacy classes — view the full character table.
| maximal subgroup of | #32914821⋊C2, C2×#32914821 |
| maximal normal subgroup of | #32914821⋊C2, C2×#32914821 |
| maximal quotient of | C2×#32914821 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18477, 3);