Finite Group DatabasebetaFinite Group Databasebeta| order | 5672 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C709 · Schur multiplier (H2) = C1 |
| direct product | Q8×C709 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C709 | C22 |
| commutator, Frattini | C2 | C22×C709 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C709 ◁ G | |
12 conjugacy classes of subgroups.
3545 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5672, 4);