Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5646 |
| Fitting | C32×C22⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ #563 |
429 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#563, C2×C3×#5646, D3×#5646, … |
| maximal normal subgroup of | C3×D3×#563, C2×C3×#5646, D3×#5646, … |
| maximal quotient of | C3×#74013, C3×#74598, C3×#76617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7625);