Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C9 ⋊ #322 |
99 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=f,d^2=e,g^3=h^2,b^a=bf,g^a=g^2h,h^a=h^2168 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#322, C2×#10588131, C8×#3663, … |
| maximal normal subgroup of | D9×#322, C2×#10588131, C8×#3663, … |
| maximal quotient of | C9⋊#1273, #11771308, #11771321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 13);