Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63961 |
| Sylow | C32 ⋊ C2×#123 |
750 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11787971, #11787974, #11788275, … |
| maximal normal subgroup of | #11787971, #11787974, #11788275, … |
| maximal quotient of | C2×#10591696, C2×#10591693, C2×#10591710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7366);