Finite Group DatabasebetaFinite Group Databasebeta| order | 18235 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C521⋊C5 |
| unambiguous semidirect product | C521⋊(C5×C7) |
| unambiguous semidirect product | (C7×C521)⋊C5 |
| Fitting, socle, Hall | C7×C521 ⋊ C5 |
| derived, Sylow | C521 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C521⋊C5 |
| commutator, cosocle, hypocenter | C521 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C521 | C5 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3647 |
763 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C521⋊C5, C7×D521⋊C5, D7×C521⋊C5, … |
| maximal normal subgroup of | C2×C7×C521⋊C5, C7×D521⋊C5, D7×C521⋊C5, … |
| maximal quotient of | C2×C7×C521⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18235, 1);