Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C271 · Schur multiplier (H2) = C22 |
| direct product | C22⋊C8×C271 |
| unambiguous semidirect product | C22⋊(C8×C271) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C271 | C22 |
| commutator | C2 | C2×C8×C271 |
| Frattini, cosocle | C2×C4 | C22×C271 |
| socle | C22×C271 | C2×C4 |
| prime radical | C23×C271 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C271 ◁ G | |
50 conjugacy classes of subgroups.
5420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 5);