Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#85563 |
| derived | C22⋊SL(2,𝔽3) ⋊ C2×C4 |
1029 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 1029 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11715706, #72227571, #72227572, … |
| maximal normal subgroup of | C2×#11715706, #72227571, #72227572, … |
| maximal quotient of | #72227572, C2×#72226630, C2×#72211558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1090035);