Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#63952 |
| Sylow | C32 ⋊ C2×C4×D4 |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11783762, #11785094, C4×#63952, … |
| maximal normal subgroup of | #11783762, #11785094, C4×#63952, … |
| maximal quotient of | C2×#10591233, C2×Dic3×#217, C2×#10591243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7356);