Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C7×C43×D29 |
| Fitting, socle, Hall | C7×C29×C43 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C7×C43 |
| Hall | C29×C43 ⋊ C2×C7 |
| Hall | C7×C29 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C43 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C7×C43 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C43 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8729 |
4816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C43×#1181, C7×C43⋊#1181, C7×D29×D43, … |
| maximal normal subgroup of | C7×C43×#1181, C7×C43⋊#1181, C7×D29×D43, … |
| maximal quotient of | C7×C43×Dic29, C2×C7×C43×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 11);