Finite Group DatabasebetaFinite Group Databasebeta| order | 2180 |
| isoclinism | isoclinic class of D5×D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D109 |
| unambiguous semidirect product | (D5×C109)⋊C2 |
| unambiguous semidirect product | (C5×D109)⋊C2 |
| unambiguous semidirect product | D545⋊C2 |
| Fitting, socle, derived, Hall | C5×C109 ⋊ C22 |
| Sylow | C109 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C109 | C22 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 114 |
| transitive degree | μt(G) = 545 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D109, C5×D5×D109, C5⋊D5×D109, … |
| maximal normal subgroup of | C5×D5×D109, C7×D5×D109, D5×C11×D109, … |
| maximal quotient of | D25×D109, C5×D5×D109, C5⋊D5×D109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2180, 12);