Finite Group DatabasebetaFinite Group Databasebeta| order | 8358 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C199 ⋊ C2×C3 |
| Hall | #16862007 ⋊ C2 |
| Hall | D7×C199 ⋊ C3 |
| Sylow | C199 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ C199⋊C3 |
| Sylow | C7 ⋊ C2×C199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C199 | C2×C3 |
| LCS | G ▷ C7×C199 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,199|c^a=c^6,c^b=c^2,d^b=d^106337 conjugacy classes — view the full character table.
| maximal subgroup of | #22552541⋊C2, C2×#22552545, AGL(1,𝔽7)×C199⋊C3, … |
| maximal normal subgroup of | #22552541⋊C2, C2×#22552545, AGL(1,𝔽7)×C199⋊C3, … |
| maximal quotient of | #30660097, C2×#22552545, #38736937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8358, 19);