Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×D4×Dic6 |
| Sylow | C32 ⋊ D4×Q8 |
607 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71014, C3×#68187, #11779231, … |
| maximal normal subgroup of | C3×#71014, C3×#68187, #11779231, … |
| maximal quotient of | C3×C22⋊C4×Dic6, C3×D4×Dic3⋊C4, C3×D4×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7516);