Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #349 |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^2,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11771409, #11771412, #11771416, … |
| maximal normal subgroup of | #11771409, #11771412, #11771416, … |
| maximal quotient of | #11771338, #11771438, #11771548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1301);