Finite Group DatabasebetaFinite Group Databasebeta| order | 18639 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C109 ⋊ C9 |
| Sylow | C109 ⋊ #4294 |
| Sylow | C19 ⋊ #11758279 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #20261880 |
| commutator, hypocenter | C19×C109 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C19×C109 | C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18639 |
Polycyclic presentation:
3,19,109,3|a^3=d,b^a=b^11,c^a=c^452079 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#32916115, #49152099, #49152103, … |
| maximal normal subgroup of | C2×#32916115, #49152099, #49152103, … |
| maximal quotient of | C2×#32916115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18639, 5);