Finite Group DatabasebetaFinite Group Databasebeta| order | 5672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic709 |
| derived, Sylow | C709 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D709 |
| commutator, hypocenter | C709 | C2×C4 |
| Frattini | C2 | C2×D709 |
| Fitting, socle | C22×C709 | C2 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×Dic709, #26015370, C22⋊Dic709, … |
| maximal normal subgroup of | C4×Dic709, #26015370, C22⋊Dic709, … |
| maximal quotient of | C4×Dic709, C22⋊Dic709, C4⋊Dic709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5672, 8);