Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C4×D4×C3⋊D3 |
| Fitting | C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×C4×D4 |
1278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D4⋊C8, #11774176, #11774180, … |
| maximal normal subgroup of | C3⋊D3×D4⋊C8, #11774176, #11774180, … |
| maximal quotient of | C4×C22⋊C4×C3⋊D3, C4×C4⋊C4×C3⋊D3, C4×#64090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7897);