Finite Group DatabasebetaFinite Group Databasebeta| order | 18550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D175 |
| unambiguous semidirect product | C7⋊(D25×C53) |
| unambiguous semidirect product | C25⋊(D7×C53) |
| Fitting, Hall | C7×C25×C53 ⋊ C2 |
| derived, Hall | C7×C25 ⋊ C2×C53 |
| Hall | C25×C53 ⋊ D7 |
| Hall | C7×C53 ⋊ D25 |
| Sylow | C25 ⋊ D7×C53 |
| Sylow | C7 ⋊ D25×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D175 |
| commutator, cosocle, hypocenter | C7×C25 | C2×C53 |
| Frattini | C5 | C53×D35 |
| Fitting | C7×C25×C53 | C2 |
| socle | C5×C7×C53 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C53 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
4717 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D175, D7×D25×C53, D175⋊D53, … |
| maximal normal subgroup of | D53×D175, D7×D25×C53, D175⋊D53, … |
| maximal quotient of | C53×Dic175, C2×C53×D175 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18550, 7);