Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C32 ⋊ #365 |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=ce,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,h^a=h^2,c^b=cf,d^b=de,e^b=ef,g^b=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4487, #11797102, C2×#10589138, … |
| maximal normal subgroup of | D3×#4487, #11797102, C2×#10589138, … |
| maximal quotient of | #11772184, #11772427, C2×#10589138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1020);