Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#63959 |
| Sylow | C32 ⋊ C2×#124 |
726 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63959, #11802387, #11802388, … |
| maximal normal subgroup of | C4×#63959, #11802387, #11802388, … |
| maximal quotient of | C2×#10591245, C2×#10591702, C2×#10591703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7364);