Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic72 |
| Sylow | C9 ⋊ C2×Q32 |
123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11772923, #11772929, #11772989, … |
| maximal normal subgroup of | #11772923, #11772929, #11772989, … |
| maximal quotient of | C2×#10588180, C2×#10588181, C4×Dic72, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 467);