Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C4×#3832 |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C4×#41 |
930 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11774229, #11774240, #11774253, … |
| maximal normal subgroup of | #11774229, #11774240, #11774253, … |
| maximal quotient of | C4×#64101, C4×#64102, C4×Q8×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7926);