Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D67 |
| commutator, socle, cosocle | C22×C67 | C23 |
| Fitting | C22⋊C4×C67 | C2 |
| hypercenter | C22⋊C4 | D67 |
| hypocenter | C67 | #120 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 536 |
Polycyclic presentation:
2^5,67|b^a=bd,c^a=ce,f^a=f^66,f^c=f^66344 conjugacy classes — view the full character table.
| maximal subgroup of | #16863584, #120×D67, C2×#14524013, … |
| maximal normal subgroup of | #16863584, #120×D67, C2×#14524013, … |
| maximal quotient of | #16863251, #16863270, #16863271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 116);