Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C7 |
| direct product | C2×#11716066 |
| Sylow | C72 ⋊ C2×M16 |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×M16×C7⋊D7, C2×#13096577, C2×#13096589, … |
| maximal normal subgroup of | C2×M16×C7⋊D7, C2×#13096577, C2×#13096589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 727);