Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×D3×Q16 |
| Fitting | C2×C32×Q16 ⋊ C2 |
| Sylow | C32 ⋊ C22×Q16 |
546 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#358, D3×#4564, C3×#69222, … |
| maximal normal subgroup of | C3×D3×#358, D3×#4564, C3×#69222, … |
| maximal quotient of | C2×C3×D3×#103, C2×C3×D3×#107, C3×C4×D3×Q16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7742);