Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C67⋊#95 |
| Sylow | C67 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D67 |
| commutator | C2×C67 | C42 |
| Fitting | C22×C4×C67 | C2 |
| socle, prime radical, cosocle | C23×C67 | C22 |
| hypercenter | C22×C4 | D67 |
| hypocenter | C67 | #95 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^5,67|a^2=d,b^2=e,b^a=bc,f^b=f^66548 conjugacy classes — view the full character table.
| maximal subgroup of | #16863130, #16863131, #16863133, … |
| maximal normal subgroup of | #16863130, #16863131, #16863133, … |
| maximal quotient of | #16863150, #16863151, #16863152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 53);