Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C4×#3830 |
| Fitting | C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C4×#41 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11774223, #11774239, #11774245, … |
| maximal normal subgroup of | #11774223, #11774239, #11774245, … |
| maximal quotient of | C4×#64086, C4×#64101, C4×#64090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7889);