Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C2×C32×Q8 ⋊ C4 |
| Sylow | C32 ⋊ #519 |
422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=f,c^2=f,d^a=df,g^a=gh,h^a=gh^2,c^b=cf,g^e=g^2,h^e=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #11786613, #11786630, #11787839, … |
| maximal normal subgroup of | #11786613, #11786630, #11787839, … |
| maximal quotient of | #11800879, #11800941, #11802678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8528);