Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C67 ⋊ C2 |
| Sylow | C67 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D67 |
| commutator, socle, cosocle | C2×C67 | C24 |
| Fitting | #41×C67 | C2 |
| hypercenter | #41 | D67 |
| hypocenter | C67 | 2−1+4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ #41 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^d=f^66347 conjugacy classes — view the full character table.
| maximal subgroup of | #16863567, #16863570, #16863577, … |
| maximal normal subgroup of | #16863567, #16863570, #16863577, … |
| maximal quotient of | #16863872, #16863873, #16863875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 193);