Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#73105 |
585 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 585 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #72253117, C22×#73105, #72342100 |
| maximal normal subgroup of | #72253117, C22×#73105 |
| maximal quotient of | #72253117, C22×#73105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087028);