Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of D181 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic181 |
| derived, Sylow | C181 ⋊ C3×C4 |
| Hall | C3×C181 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D181 |
| commutator, hypocenter | C181 | C3×C4 |
| Frattini | C2 | C3×D181 |
| Fitting, socle, prime radical | C2×C3×C181 | C2 |
| cosocle | C2×C181 | C2×C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 188 |
| transitive degree | μt(G) = 2172 |
552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic181, C3×Dic905, C3×Dic181⋊C5, … |
| maximal normal subgroup of | C3×C5×Dic181, C3×Dic181⋊C5, C3×C7×Dic181, … |
| maximal quotient of | C3×C5×Dic181, C3×Dic905, C3×#16813739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 5);