Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C31 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic5×C31 |
| derived, Sylow | C5 ⋊ C32×C4×C31 |
| Hall | C32×C5×C31 ⋊ C4 |
| Hall | C5×C31 ⋊ C32×C4 |
| Hall | C32×C5 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C31 | D5 |
| commutator, hypocenter | C5 | C32×C4×C31 |
| Frattini | C2 | C32×D5×C31 |
| Fitting, socle | C2×C32×C5×C31 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C32×C31 | |
72 conjugacy classes of subgroups.
2232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C31×Dic25, C32×Dic5×ΓL(1,𝔽32), C32×C31×#1039, … |
| maximal normal subgroup of | C32×Dic5×ΓL(1,𝔽32), C32×C5×Dic5×C31 |
| maximal quotient of | C32×C31×Dic25, C32×C31×#1039, C32×C5×Dic5×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 76);