Finite Group DatabasebetaFinite Group Databasebeta| order | 1688 |
| isoclinism | isoclinic class of D211 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D211 |
| Fitting | C4×C211 ⋊ C2 |
| derived, Sylow | C211 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D211 |
| commutator, hypocenter | C211 | C2×C4 |
| Frattini | C2 | C2×D211 |
| Fitting | C4×C211 | C2 |
| socle, cosocle | C2×C211 | C22 |
| prime radical | C2×D211 | C2 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 844 |
428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D211, #16809945, C2×C4×D211, … |
| maximal normal subgroup of | C8×D211, #16809945, C2×C4×D211, … |
| maximal quotient of | C4×Dic211, (C2×D211)⋊C4, Dic211⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1688, 7);