Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #87656⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#87656⋊C2 |
| unambiguous semidirect product | #87656⋊C22 |
| unambiguous semidirect product | (#5997⋊C2)⋊C22 |
| Fitting, socle | C2×C72 ⋊ D8 |
| Sylow | C72 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #87656⋊C2 |
| commutator, cosocle | #5997 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72 | D8 |
| hypocenter | C72 | C2×D8 |
| LCS | G ▷ #5997 ▷ C7⋊D7 ▷ C72 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
38 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 917);