Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| isoclinism | isoclinic class of D31⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D31⋊C5 |
| unambiguous semidirect product | (C2×C32×D31)⋊C5 |
| Fitting, socle | C2×C32×C31 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C22×C32×C5 |
| Hall | C32×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×C32×D31 ⋊ C5 |
| Hall | C32×C31 ⋊ C22×C5 |
| Hall | ΓL(1,𝔽32) ⋊ C22×C32 |
| Hall | C2×D31 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D31⋊C5 |
| commutator, hypocenter | C31 | C22×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D5×D31⋊C5, C2×C32×C5×D31⋊C5, C2×C32×C5⋊(D31⋊C5) |
| maximal normal subgroup of | C2×C32×C5×D31⋊C5 |
| maximal quotient of | C2×C32×D31⋊C25, C32×D5×D31⋊C5, C2×C32×C5×D31⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 113);