Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #520 |
626 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=f,d^a=df,h^a=h^2,c^b=cf,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | #11786686, #11786695, #11786698, … |
| maximal normal subgroup of | #11786686, #11786695, #11786698, … |
| maximal quotient of | #11800884, #11800894, #11800917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6868);