Finite Group DatabasebetaFinite Group Databasebeta| order | 2180 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D109 |
| unambiguous semidirect product | C109⋊(C22×C5) |
| unambiguous semidirect product | (C2×C109)⋊(C2×C5) |
| Fitting, socle | C2×C5×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C22×C5 |
| Hall | C5×C109 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D109 |
| commutator, cosocle, hypocenter | C109 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1090 |
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×D109, C5×D5×D109, C2×C5×D545, … |
| maximal normal subgroup of | C2×C25×D109, C2×C52×D109, C2×C5×C7×D109, … |
| maximal quotient of | C2×C25×D109, C5×D5×D109, C2×C5×D545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2180, 15);