Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C16×Dic67 |
| derived, Sylow | C67 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D67 |
| commutator, hypocenter | C67 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | C22×C16×C67 | C2 |
| socle | C23×C67 | C2×C8 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C22×C16 | |
216 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743517, #30743521, C4×C16×Dic67, … |
| maximal normal subgroup of | #30743517, #30743521, C4×C16×Dic67, … |
| maximal quotient of | C2×C16×C67⋊C8, C2×#22558128, C16×#11761612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6096);