Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#73149 |
1193 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1193 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | #72267941, C2×#72227572 |
| maximal normal subgroup of | #72267941 |
| maximal quotient of | C2×#72227572 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086993);