Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×#22576608 |
| Fitting, socle, Hall | C2×C29×C43 ⋊ C7 |
| derived, Hall | C29×C43 ⋊ C2×C7 |
| Hall | C2×C43 ⋊ C29⋊C7 |
| Hall | C2×C29 ⋊ C43⋊C7 |
| Sylow | C43 ⋊ C2×C29⋊C7 |
| Sylow | C29 ⋊ C2×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22576608 |
| commutator, cosocle, hypocenter | C29×C43 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C43 | C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2494 |
370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22576608, #46853593, #46853601, … |
| maximal normal subgroup of | C4×#22576608, #46853593, #46853601, … |
| maximal quotient of | C4×#22576608, C22×#22576608 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 6);