Finite Group DatabasebetaFinite Group Databasebeta| order | 18410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1315 |
| unambiguous semidirect product | C5⋊(C7×D263) |
| unambiguous semidirect product | C263⋊(C7×D5) |
| Fitting, socle, Hall | C5×C7×C263 ⋊ C2 |
| derived, Hall | C5×C263 ⋊ C2×C7 |
| Hall | C7×C263 ⋊ D5 |
| Sylow | C263 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ D263 |
| Sylow | C5 ⋊ C7×D263 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1315 |
| commutator, cosocle, hypocenter | C5×C263 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C263 | C2 |
| LCS | G ▷ C5×C263 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9205 |
4613 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×D263, D7×D1315, D35⋊D263, … |
| maximal normal subgroup of | C7×D5×D263, D7×D1315, D35⋊D263, … |
| maximal quotient of | C7×Dic1315, C2×C7×D1315 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18410, 6);