Finite Group DatabasebetaFinite Group Databasebeta| order | 5620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D281 |
| Fitting, socle | C2×C5×C281 ⋊ C2 |
| derived, Sylow | C281 ⋊ C22×C5 |
| Hall | C5×C281 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D281 |
| commutator, hypocenter | C281 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C281 | C2 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
1420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D281, C2×C5×D843, C2×C3×C5×D281, … |
| maximal normal subgroup of | C2×C3×C5×D281, C2×D281⋊C25, C2×C25×D281, … |
| maximal quotient of | C5×D3×D281, C2×C5×D843, C2×C3×C5×D281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5620, 20);