Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C53 · Schur multiplier (H2) = C1 |
| direct product | C2×C53×#4296 |
| Fitting, socle, Hall | C2×C19×C53 ⋊ C9 |
| derived, Sylow | C19 ⋊ C2×C9×C53 |
| Hall | C19×C53 ⋊ C2×C9 |
| Hall | C2×C19 ⋊ C9×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | #4296 |
| commutator, hypocenter | C19 | C2×C9×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C53 | C9 |
| prime radical | C2×C53×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C2×C3×C53 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2014 |
1166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#4296⋊C4, #4296⋊Dic53, #4296×Dic53, … |
| maximal normal subgroup of | C53×#4296⋊C4, #4296⋊Dic53, #4296×Dic53, … |
| maximal quotient of | C4×C53×#4296, C22×C53×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 17);