Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#803 |
| Sylow | C32 ⋊ C2×#97 |
346 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67740, #11770726, C3×#67741, … |
| maximal normal subgroup of | C3×#67740, #11770726, C3×#67741, … |
| maximal quotient of | C2×C3×#4454, C3×#69847, C3×#69726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3900);