Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #441 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=e,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=cd,d^b=df,d^c=df78 conjugacy classes — view the full character table.
| maximal subgroup of | #11797898, #11797904, #11797921, … |
| maximal normal subgroup of | #11797898, #11797904, #11797921, … |
| maximal quotient of | #11777304, #11777660, #11777919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4434);