Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#63955 |
| Sylow | C32 ⋊ C2×#117 |
726 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11783376, #11783378, #11785707, … |
| maximal normal subgroup of | #11783376, #11783378, #11785707, … |
| maximal quotient of | C2×#10591239, C2×Dic3×#217, C2×#10591242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7360);