Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×Q8×A4 |
| Fitting | C23×C3×Q8 ⋊ C3 |
| Sylow | C23×Q8 ⋊ C32 |
486 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×#101, C3×A4×#103, C3×C4×Q8×A4, … |
| maximal normal subgroup of | C3×A4×#101, C3×A4×#103, C3×C4×Q8×A4, … |
| maximal quotient of | C2×C3×A4×C4⋊C4, C3×C4×Q8×A4, C3×A4×C22⋊Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8594);