Finite Group DatabasebetaFinite Group Databasebeta| order | 2220 |
| isoclinism | isoclinic class of D5×D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C5×C37 ⋊ C22×C3 |
| Hall | D5×D37 ⋊ C3 |
| Hall | C5×C37⋊C3 ⋊ C22 |
| Hall | C37⋊C3 ⋊ C2×D5 |
| Sylow | C37 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C37 | C22×C3 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 185 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D37⋊C3, C5×D5×D37⋊C3, C5⋊D5×D37⋊C3, … |
| maximal normal subgroup of | C5×D5×D37⋊C3, C7×D5×D37⋊C3, D5×C11×D37⋊C3, … |
| maximal quotient of | D25×D37⋊C3, C5×D5×D37⋊C3, C5⋊D5×D37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2220, 20);