Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D67 |
| unambiguous semidirect product | C67⋊C27 |
| unambiguous semidirect product | (C2×C67)⋊C26 |
| Fitting, socle | C26×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D67 |
| commutator, hypocenter | C67 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30786986, C2×#379×D67, C22×#16863251, … |
| maximal normal subgroup of | #30786986, C2×#379×D67, C22×#16863251, … |
| maximal quotient of | C25×C4×D67, C26×Dic67, C24×D4×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19324);