Finite Group DatabasebetaFinite Group Databasebeta| order | 17458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D29×C43⋊C7 |
| Fitting, socle, derived, Hall | C29×C43 ⋊ C2×C7 |
| Hall | C29×C43⋊C7 ⋊ C2 |
| Hall | C43×D29 ⋊ C7 |
| Sylow | C43 ⋊ C7×D29 |
| 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 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | (C43⋊C7)⋊#1181, #1181×C43⋊C7, D29×D43⋊C7, … |
| maximal normal subgroup of | (C43⋊C7)⋊#1181, #1181×C43⋊C7, D29×D43⋊C7, … |
| maximal quotient of | Dic29×C43⋊C7, C2×D29×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17458, 25);