Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of D181 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D181 |
| Fitting, socle | C2×C3×C181 ⋊ C2 |
| derived, Sylow | C181 ⋊ C22×C3 |
| Hall | C3×C181 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D181 |
| commutator, cosocle, hypocenter | C181 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C181 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1086 |
552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×D181⋊C5, C3×D5×D181, C2×C3×D905, … |
| maximal normal subgroup of | C2×C3×D181⋊C5, C2×C3×C5×D181, C2×C3×C7×D181, … |
| maximal quotient of | C3×D5×D181, C2×C3×D905, C2×C3×C5×D181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 16);