Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C67 ⋊ C2 |
| Sylow | C67 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D67 |
| commutator, socle | C2×C67 | C2×C8 |
| Fitting | C16×C67 | C2 |
| prime radical | C2×D67 | C8 |
| cosocle | C8×C67 | C22 |
| hypercenter | C16 | D67 |
| hypocenter | C67 | M32 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1072 |
Polycyclic presentation:
2^5,67|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^66548 conjugacy classes — view the full character table.
| maximal subgroup of | M32×D67, C2×#14523982, #16863812, … |
| maximal normal subgroup of | M32×D67, C2×#14523982, #16863812, … |
| maximal quotient of | #16863171, (C2×D67)⋊C16, Dic67⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 85);