Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #327 |
117 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 117 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=ef,b^a=bcd,d^a=df,g^a=g^2h^2,h^a=g^2,c^b=ce,d^b=df,g^b=gh^2,h^b=h^2,g^c=g^2h,h^c=gh,g^d=g^2,h^d=h^2,g^e=g^2,h^e=h^224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593164, #11775070, #11775532, … |
| maximal normal subgroup of | C2×#10593164, #11775070, #11775532, … |
| maximal quotient of | #11770663, #11770682, #11771061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5046);