Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#64225 |
| Sylow | C32 ⋊ C22×D8 |
574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #11787557, #11791049, #11791115, … |
| maximal normal subgroup of | #11787557, #11791049, #11791115, … |
| maximal quotient of | C2×#10593365, C2×#10593396, C2×#10593420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8380);