Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×#108 ⋊ C2 |
| Sylow | C9 ⋊ #430 |
153 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,e^2=f,g^3=h^2,b^a=bf,g^a=g^2h,h^a=h^2,c^b=ce,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11799975, #11799984, #11800007, … |
| maximal normal subgroup of | #11799975, #11799984, #11800007, … |
| maximal quotient of | #11776825, #11776831, #11776935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 455);