Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C5×C3⋊D3×C41⋊C5 |
| unambiguous semidirect product | C3⋊(C5×D3×C41⋊C5) |
| unambiguous semidirect product | (C3⋊D3×C41)⋊C52 |
| unambiguous semidirect product | (C5×C3⋊D3×C41)⋊C5 |
| Fitting, socle | C32×C5×C41 ⋊ C2×C5 |
| derived, Hall | C32×C41 ⋊ C2×C52 |
| Hall | C32×C5×C41⋊C5 ⋊ C2 |
| Hall | C3⋊D3×C41 ⋊ C52 |
| Sylow | C41 ⋊ C52×C3⋊D3 |
| Sylow | C32 ⋊ C2×C5×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D3×C41⋊C5 |
| commutator, cosocle, hypocenter | C32×C41 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C2×C5 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C5 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#13093288⋊C5, C5×#157×C41⋊C5, #20301658⋊C5, … |
| maximal normal subgroup of | C5×#13093288⋊C5, C5×#157×C41⋊C5, #20301658⋊C5, … |
| maximal quotient of | C5×C3⋊Dic3×C41⋊C5, C2×C5×C3⋊D3×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 66);