Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3×C4 |
| direct product | C2×#64286 |
| Fitting | C22×C32×C4 ⋊ C4 |
| Sylow | C32 ⋊ C2×#117 |
566 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #11773771, #11783107, #11783110, … |
| maximal normal subgroup of | #11773771, #11783107, #11783110, … |
| maximal quotient of | C2×#10593733, C2×C4×C22⋊#157, C2×C4×C4⋊#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8520);