Finite Group DatabasebetaFinite Group Databasebeta| order | 10820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic541 |
| derived, Sylow | C541 ⋊ C4×C5 |
| Hall | C5×C541 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D541 |
| commutator, hypocenter | C541 | C4×C5 |
| Frattini | C2 | C5×D541 |
| Fitting, socle, prime radical | C2×C5×C541 | C2 |
| cosocle | C2×C541 | C2×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic541, C5×Dic1623, C5×Dic541⋊C3 |
| maximal normal subgroup of | C3×C5×Dic541, C5×Dic541⋊C3 |
| maximal quotient of | C3×C5×Dic541, C5×Dic1623 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 5);