Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C8×D4 |
293 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,b^a=be,h^a=h^2,c^b=ce,g^b=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #11859164, D3×C8×#67, C2×#10590720, … |
| maximal normal subgroup of | #11859164, D3×C8×#67, C2×#10590720, … |
| maximal quotient of | #11777148, #11777189, #11777206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2602);