Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#63359 |
| Fitting | C2×C9×C16 ⋊ C2 |
| Sylow | C9 ⋊ C2×SD32 |
135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #11797654, C4×#63359, #11797730, … |
| maximal normal subgroup of | #11797654, C4×#63359, #11797730, … |
| maximal quotient of | C2×#10588186, C2×#10588180, C2×#10588182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 465);