Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic67 |
| derived, Sylow | C67 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D67 |
| commutator, hypocenter | C67 | C4×C8 |
| Frattini | C2×C4 | C2×D67 |
| Fitting | C2×C8×C67 | C2 |
| socle, prime radical | C22×C67 | C2×C4 |
| cosocle | C2×C4×C67 | C22 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2144 |
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic67, #16863171, Dic67⋊C16, … |
| maximal normal subgroup of | C16×Dic67, #16863171, Dic67⋊C16, … |
| maximal quotient of | C8×C67⋊C8, #16863118, #16863150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 54);