Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D67 |
| unambiguous semidirect product | C67⋊C25 |
| unambiguous semidirect product | (C2×C67)⋊C24 |
| Fitting, socle | C24×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D67 |
| commutator, cosocle, hypocenter | C67 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1072 |
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16863251, C2×C22⋊C4×D67, C22×(C2×D67)⋊C4, … |
| maximal normal subgroup of | #16863251, C2×C22⋊C4×D67, C22×(C2×D67)⋊C4, … |
| maximal quotient of | C23×C4×D67, C24×Dic67, C22×D4×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 195);