Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C4×M16 |
306 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=d,c^2=e,e^2=f,c^a=cf,h^a=h^2,c^b=cf,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | #11797393, C4×#63791, D3×Dic3×M16, … |
| maximal normal subgroup of | #11797393, C4×#63791, D3×Dic3×M16, … |
| maximal quotient of | #11773543, #11773551, #11773604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2549);