Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×#994 |
| Fitting, Sylow | C2×C4×H(5,𝔽2) ⋊ C3 |
2508 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 373 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#994, C2×C4×Ω+(4,𝔽3) |
| maximal normal subgroup of | C2×C4×Ω+(4,𝔽3) |
| maximal quotient of | C2×AGL(1,𝔽5)×#994 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084977);