Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of D15×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived | C23×C3×C5 ⋊ C2×C7 |
| Hall | C23×D15 ⋊ C7 |
| Hall | C3×C5 ⋊ C2×AGL(1,𝔽8) |
| Sylow | C5 ⋊ D3×AGL(1,𝔽8) |
| Sylow | C3 ⋊ D5×AGL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C3×C5 | C2×C7 |
| LCS | G ▷ C23×C3×C5 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 942);