Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C5 |
| direct product | D3×C41×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C41×C52⋊C3) |
| unambiguous semidirect product | (C52×D3)⋊(C3×C41) |
| unambiguous semidirect product | (C52×D3×C41)⋊C3 |
| Fitting, socle | C3×C52×C41 ⋊ C2×C3 |
| derived | C3×C52 ⋊ 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 | C41 | D3×C52⋊C3 |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C41 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
1353 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C52⋊C3×D41, D3×C41×#3874, D3×C41⋊#3874, … |
| maximal normal subgroup of | D3×C52⋊C3×D41, D3×C41×#3874, D3×C41⋊#3874, … |
| maximal quotient of | Dic3×C41×C52⋊C3, C2×D3×C41×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 78);