Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of #4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×#4380 |
| Fitting, socle, Hall | C32×C5×C41 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C41 |
| Hall | C32×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ #157 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C41 |
| Sylow | C5 ⋊ #157×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #4380 |
| commutator, hypocenter | C32×C5 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C4 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C41 | |
40 conjugacy classes of subgroups.
615 conjugacy classes — view the full character table.
| maximal subgroup of | C41×#11744621, #4380×C41⋊C5, C5×C41×#4380, … |
| maximal normal subgroup of | #4380×C41⋊C5, C5×C41×#4380 |
| maximal quotient of | C41×#11744621, C5×C41×#4380, C41×#11744709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 130);