Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63951 |
| Sylow | C32 ⋊ C2×#137 |
594 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11860386, #11860392, C4×#63951, … |
| maximal normal subgroup of | #11860386, #11860392, C4×#63951, … |
| maximal quotient of | C2×#10591562, C2×#10590612, C2×#10590583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7218);