Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#5727 |
| Fitting | C32×C4⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ D4×Q8 |
594 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71205, C3×#68457, #11779219, … |
| maximal normal subgroup of | C3×#71205, C3×#68457, #11779219, … |
| maximal quotient of | C3×#76614, C3×#74360, C3×#76202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7706);