Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C7 |
| direct product | C22×C7⋊(C7⋊C8) |
| derived, Sylow | C72 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C7⋊D7 |
| commutator, hypocenter | C72 | C22×C8 |
| Frattini | C4 | C22×C7⋊D7 |
| Fitting | C22×C4×C72 | C2 |
| socle, prime radical | C23×C72 | C4 |
| cosocle | C4×C72 | C23 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C4 | |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1568 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 726);