Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #479 |
109 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 109 conjugacy classes of subgroups — too many to draw. Only its 31 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|a^2=d,b^2=d,c^2=f,e^2=f,b^a=bdf,g^a=g^2h^2,h^a=g^2h,c^b=ce,e^b=ef,g^b=gh^2,h^b=g^2h^2,e^c=ef,g^d=g^2,h^d=h^224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593560, #11868634, #11868774, … |
| maximal normal subgroup of | C2×#10593560, #11868634, #11868774, … |
| maximal quotient of | #11785297, #11786906, #11787003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5442);