Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #368 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=de,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,g^a=gh,h^a=gh^2,g^c=g^2,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #11772954, #11772982, #11772998, … |
| maximal normal subgroup of | #11772954, #11772982, #11772998, … |
| maximal quotient of | #11772224, #11772236, #11772386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2023);