Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D67 |
| commutator, socle, cosocle | C22×C67 | C23 |
| Fitting | C22⋊C4×C67 | C2 |
| prime radical | C2×C22⋊D67 | C2 |
| hypercenter | C22⋊C4 | D67 |
| hypocenter | C67 | #123 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|c^2=d,b^a=bd,c^a=ce,f^b=f^66344 conjugacy classes — view the full character table.
| maximal subgroup of | #123×D67, C2×#14524025, #16863905, … |
| maximal normal subgroup of | #123×D67, C2×#14524025, #16863905, … |
| maximal quotient of | #16863258, #16863270, #16863272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 128);