Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C43 ⋊ C2×C7 |
| Hall | #22576608 ⋊ C2 |
| Hall | C43×D29 ⋊ C7 |
| Hall | D29 ⋊ C43⋊C7 |
| Sylow | C43 ⋊ D29⋊C7 |
| Sylow | C29 ⋊ C2×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C43 | C2×C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1247 |
Polycyclic presentation:
2,7,29,43|c^a=c^28,c^b=c^16,d^b=d^35112 conjugacy classes — view the full character table.
| maximal subgroup of | #46853619, #46853625, #31775443⋊C2, … |
| maximal normal subgroup of | #46853619, #46853625, #31775443⋊C2, … |
| maximal quotient of | #46853601, C2×#31775451 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 29);