Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C2×Q32 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,h^a=h^2,c^b=cd,d^b=de,e^b=ef,g^b=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11772937, #11773003, #11799217, … |
| maximal normal subgroup of | #11772937, #11773003, #11799217, … |
| maximal quotient of | #11796628, #11797160, #11797718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2122);