Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic155 |
| derived, Hall | C5×C31 ⋊ C32×C4 |
| Hall | C32×C5×C31 ⋊ C4 |
| Hall | C32×C31 ⋊ Dic5 |
| Hall | C32×C5 ⋊ Dic31 |
| Sylow | C31 ⋊ C32×Dic5 |
| Sylow | C5 ⋊ C32×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D155 |
| commutator, hypocenter | C5×C31 | C32×C4 |
| Frattini | C2 | C32×D155 |
| Fitting, socle | C2×C32×C5×C31 | C2 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
1422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic775, C32×ΓL(1,𝔽32)⋊Dic5, C32×C31⋊#1039, … |
| maximal normal subgroup of | C32×ΓL(1,𝔽32)⋊Dic5, C32×C5×Dic155 |
| maximal quotient of | C32×Dic775, C32×C31⋊#1039, C32×C5×Dic155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 77);