Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D67 |
| commutator | C2×C67 | C22×C4 |
| Fitting | C4⋊C4×C67 | C2 |
| socle, cosocle | C22×C67 | C23 |
| prime radical | C2×D268 | C2 |
| hypercenter | C4⋊C4 | D67 |
| hypocenter | C67 | C4×D4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=e,c^2=e,b^a=bd,f^b=f^66,f^c=f^66350 conjugacy classes — view the full character table.
| maximal subgroup of | #16863476, #16863478, #16863481, … |
| maximal normal subgroup of | #16863476, #16863478, #16863481, … |
| maximal quotient of | #16863243, C4⋊C4×Dic67, #16863267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 108);