Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C67 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#108×C67 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C67 | D4 |
| commutator | C4 | C2×C42×C67 |
| Frattini, cosocle | C22×C4 | C23×C67 |
| socle | C22×C67 | C2×C4⋊C4 |
| prime radical | C23×C67 | C2×Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C67 ◁ C2×C42×C67 ◁ G | |
228 conjugacy classes of subgroups.
3752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 509);