Finite Group DatabasebetaFinite Group Databasebeta| order | 17178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C409⋊C3)⋊D7 |
| Fitting, socle, derived, Hall | C7×C409 ⋊ C2×C3 |
| Hall | C7×C409⋊C3 ⋊ C2 |
| Hall | D2863 ⋊ C3 |
| Hall | C409⋊C3 ⋊ D7 |
| Sylow | C409 ⋊ C3×D7 |
| Sylow | C7 ⋊ D409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C409 | C2×C3 |
| LCS | G ▷ C7×C409 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2863 |
Polycyclic presentation:
2,3,7,409|c^a=c^6,d^a=d^408,d^b=d^355491 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D409⋊C3, C2×(C409⋊C3)⋊D7 |
| maximal normal subgroup of | D7×D409⋊C3, C2×(C409⋊C3)⋊D7 |
| maximal quotient of | #46805272, C2×(C409⋊C3)⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17178, 21);