Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#6379 |
| Fitting | C42×C72 ⋊ C2 |
| Sylow | C72 ⋊ #104 |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72214768, #72214827, C7×#89849, … |
| maximal normal subgroup of | #72214768, #72214827, C7×#89849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 248);