Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×C3⋊C8 |
| Sylow | C32 ⋊ C8×D4 |
315 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#68148, C3×D8×C3⋊C8, C3⋊C8×#213, … |
| maximal normal subgroup of | C3×#68148, C3×D8×C3⋊C8, C3⋊C8×#213, … |
| maximal quotient of | C3×D8×C3⋊C8, C3×SD16×C3⋊C8, C3×Q16×C3⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3989);