Finite Group DatabasebetaFinite Group Databasebeta| order | 8358 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C199⋊C3)⋊D7 |
| Fitting, socle, derived, Hall | C7×C199 ⋊ C2×C3 |
| Hall | C7×C199⋊C3 ⋊ C2 |
| Hall | D1393 ⋊ C3 |
| Hall | C199⋊C3 ⋊ D7 |
| Sylow | C199 ⋊ C3×D7 |
| Sylow | C7 ⋊ D199⋊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,d^a=d^198,d^b=d^106246 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D199⋊C3, C2×(C199⋊C3)⋊D7, #38736945, … |
| maximal normal subgroup of | D7×D199⋊C3, C2×(C199⋊C3)⋊D7, #38736945, … |
| maximal quotient of | (C199⋊C3)⋊Dic7, C2×(C199⋊C3)⋊D7, #13184224⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8358, 21);