Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C4⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ #518 |
723 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|c^2=f,d^2=e,d^a=df,h^a=h^2,c^b=cf,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11860539, #11860541, #11860542, … |
| maximal normal subgroup of | #11860539, #11860541, #11860542, … |
| maximal quotient of | #11800859, #11800888, #11800919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6486);