Finite Group DatabasebetaFinite Group Databasebeta| order | 11420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic571 |
| derived, Sylow | C571 ⋊ C4×C5 |
| Hall | C5×C571 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D571 |
| commutator, hypocenter | C571 | C4×C5 |
| Frattini | C2 | C5×D571 |
| Fitting, socle, prime radical | C2×C5×C571 | C2 |
| cosocle | C2×C571 | C2×C5 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
2870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic571, C5×Dic1713, C5×(C571⋊C3)⋊C4 |
| maximal normal subgroup of | C3×C5×Dic571, C5×(C571⋊C3)⋊C4 |
| maximal quotient of | C3×C5×Dic571, C5×Dic1713 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11420, 5);