Finite Group DatabasebetaFinite Group Databasebeta| order | 2172 |
| isoclinism | isoclinic class of #10624382⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624382⋊C3 |
| Fitting, socle, derived, Sylow | C181 ⋊ C3×C4 |
| Hall | #10624382 ⋊ C3 |
| Hall | C181⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C181 | C3×C4 |
| prime radical | D181⋊C3 | C2 |
| cosocle | D181 | C2×C3 |
| LCS | G ▷ C181 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 181 |
Polycyclic presentation:
2,3,2,181|a^2=c,d^a=d^162,d^b=d^132,d^c=d^18027 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2172, 8);