Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C2×D16 |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=ef,d^2=ef,e^2=f,b^a=bd,c^a=ce,d^a=de,e^a=ef,g^a=g^2,c^b=ce,d^b=de,e^b=ef,g^b=h,h^b=g,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11772922, #11772988, #11798072, … |
| maximal normal subgroup of | #11772922, #11772988, #11798072, … |
| maximal quotient of | #11796604, #11797164, #11797647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5158);