Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #499 |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=df,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,h^a=h^2,c^b=ce,e^b=ef,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11772105, #11772156, #11799649, … |
| maximal normal subgroup of | #11772105, #11772156, #11799649, … |
| maximal quotient of | #11786258, #11790108, #11790148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2756);