Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #519 |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=f,c^2=f,d^a=df,g^a=g^2,h^a=h^2,c^b=cf114 conjugacy classes — view the full character table.
| maximal subgroup of | #11785933, #11785946, #11786602, … |
| maximal normal subgroup of | #11785933, #11785946, #11786602, … |
| maximal quotient of | #11800876, #11800939, #11802676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8165);