Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×#3874 |
| Fitting, socle | C3×C52×C41 ⋊ D3 |
| derived | C52⋊C3 ⋊ C2×C3×C41 |
| Hall | C3×C41×C52⋊C3 ⋊ C2 |
| Hall | C52×C41 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C41 |
| Sylow | C52 ⋊ C3×D3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3×C41 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
1599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D41×#3874, C3×C41×#3874⋊C2, C3×#3874⋊D41, … |
| maximal normal subgroup of | C3×D41×#3874, C3×C41×#3874⋊C2, C3×#3874⋊D41, … |
| maximal quotient of | C3×C41×#64470, C2×C3×C41×#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 69);