Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#63913 |
| Sylow | C32 ⋊ C2×#124 |
738 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11787917, #11792125, C2×#10590059, … |
| maximal normal subgroup of | #11787917, #11792125, C2×#10590059, … |
| maximal quotient of | C2×#10591247, C2×#10591281, C2×#10591316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6897);