Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#11717961 |
| Fitting, socle, Hall | C32×C5×C41 ⋊ C4 |
| derived, Hall | C5×C41 ⋊ C32×C4 |
| Hall | C32×C41 ⋊ AGL(1,𝔽5) |
| Hall | C32×C5 ⋊ #4223 |
| Sylow | C41 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C32×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #11717961 |
| commutator, hypocenter | C5×C41 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C4 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
495 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#16861480, C32×#11717961⋊C5, C32×C5×#11717961, … |
| maximal normal subgroup of | C32×#11717961⋊C5, C32×C5×#11717961 |
| maximal quotient of | C32×#16861480, C32×C5×#11717961, C32×#16861525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 88);