Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#3811 |
| Fitting | C22×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×C4×D4 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11773800, #11773801, #11773936, … |
| maximal normal subgroup of | #11773800, #11773801, #11773936, … |
| maximal quotient of | C4×#63974, C4×#63921, C4×#63883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6939);