Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #341 |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=de,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=gh,h^a=gh^2,g^c=g^2,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11771890, #11771891, #11771896, … |
| maximal normal subgroup of | #11771890, #11771891, #11771896, … |
| maximal quotient of | #11770753, #11770771, #11770940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2067);