Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #87648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | C4×C4⋊(C7⋊D7) |
| Fitting | C42×C72 ⋊ C2 |
| Sylow | C72 ⋊ C4×D4 |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72259436, C4×D4×C7⋊D7, #72259541, … |
| maximal normal subgroup of | #72259436, C4×D4×C7⋊D7, #72259541, … |
| maximal quotient of | #72259436 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 679);