Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | Q8×#1020 |
| Fitting | C24×Q8 ⋊ D3 |
1654 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 1654 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | Q8×A4⋊S4, SD16×#1020, SL(2,𝔽3)×#1020, … |
| maximal normal subgroup of | SD16×#1020, SL(2,𝔽3)×#1020, Q8×#1020⋊C2, … |
| maximal quotient of | C4⋊C4×#1020, Q8×#5934 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1090185);