Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D7×C7⋊C16 |
| unambiguous semidirect product | (C7×D7)⋊C16 |
| derived, Sylow | C72 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D72 |
| commutator, hypocenter | C72 | C2×C16 |
| Fitting, cosocle | C72×C8 | C22 |
| socle | C2×C72 | C2×C8 |
| prime radical | C2×C7×D7 | C8 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C8 | |
71 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 199);