Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×Q16×C3⋊D3 |
| Fitting | C2×C32×Q16 ⋊ C2 |
| Sylow | C32 ⋊ C22×Q16 |
774 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11787486, #11791001, #11791067, … |
| maximal normal subgroup of | #11787486, #11791001, #11791067, … |
| maximal quotient of | C2×C3⋊D3×#103, C2×C3⋊D3×#107, C4×Q16×C3⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8116);