Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic3×Dic12 |
| Sylow | C32 ⋊ C4×Q16 |
238 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #11797672, #11797681, Dic3×#827, … |
| maximal normal subgroup of | #11797672, #11797681, Dic3×#827, … |
| maximal quotient of | C3⋊C8×Dic12, #11777554, #11777861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2688);