Finite Group DatabasebetaFinite Group Databasebeta| order | 7455 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived, Hall | C7×C71 ⋊ C3×C5 |
| Hall | C7×C71⋊C5 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C71 ⋊ C5 |
| Sylow | C71 ⋊ C5×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C71 | C3×C5 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7455, 6);