Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#85544 |
| Fitting | C2×#585 ⋊ D3 |
1733 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1733 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11923520, C2×#11714723, #72226188, … |
| maximal normal subgroup of | C2×#11714723, #72226188, C2×#11715001, … |
| maximal quotient of | #72226333, #72258754, C4×#85544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1089098);