Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×#64269⋊C3 |
| unambiguous semidirect product | (C2×#64269)⋊C3 |
| Fitting | C25×C32 ⋊ D3 |
1208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 1208 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213301, C2×#13164261, C22×#64269⋊C3, … |
| maximal normal subgroup of | C2×#13164261, C22×#64269⋊C3, C4×#64269⋊C3 |
| maximal quotient of | C22×#64269⋊C3, C2×#10593663⋊C3, C4×#64269⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30511);