Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D67 |
| commutator, socle | C2×C67 | C22×C4 |
| Fitting, prime radical | #41×C67 | C2 |
| cosocle | C4×C67 | C23 |
| hypercenter | #41 | D67 |
| hypocenter | C67 | #131 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=d,d^2=e,f^a=f^66,c^b=ce350 conjugacy classes — view the full character table.
| maximal subgroup of | #16863510, #16863513, #16863515, … |
| maximal normal subgroup of | #16863510, #16863513, #16863515, … |
| maximal quotient of | #16863352, #16863363, #16863423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 153);