Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6258 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22×#88613 |
| derived | C22⋊H(3,𝔽3) ⋊ C22×C4 |
1384 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1384 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11722398 |
| maximal normal subgroup of | C22×#11722398 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30573);