Finite Group DatabasebetaFinite Group Databasebeta| order | 2168 |
| isoclinism | isoclinic class of D271 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic271 |
| unambiguous semidirect product | (C2×C271)⋊C4 |
| derived, Sylow | C271 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D271 |
| commutator, hypocenter | C271 | C2×C4 |
| Frattini | C2 | C2×D271 |
| Fitting, socle, prime radical | C22×C271 | C2 |
| cosocle | C2×C271 | C22 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2168 |
548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic271, (C2×D271)⋊C4, C22⋊Dic271, … |
| maximal normal subgroup of | C4×Dic271, (C2×D271)⋊C4, C22⋊Dic271, … |
| maximal quotient of | C4×Dic271, C22⋊Dic271, C4⋊Dic271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2168, 8);