Finite Group DatabasebetaFinite Group Databasebeta| order | 11420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D571 |
| unambiguous semidirect product | (D5×C571)⋊C2 |
| unambiguous semidirect product | (C5×D571)⋊C2 |
| unambiguous semidirect product | D2855⋊C2 |
| Fitting, socle, derived, Hall | C5×C571 ⋊ C22 |
| Sylow | C571 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D571 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C571 | C22 |
| LCS | G ▷ C5×C571 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D571⋊C3, C3×D5×D571, D15×D571, … |
| maximal normal subgroup of | D5×D571⋊C3, C3×D5×D571 |
| maximal quotient of | C3×D5×D571, D15×D571, D5×D1713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11420, 12);