Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×D8 ⋊ C4 |
| Sylow | C32 ⋊ #443 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,d^2=f,e^2=f,g^a=gh,h^a=gh^2,c^b=ce,e^b=ef,e^c=ef,g^d=g^2,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | #11771649, #11771668, #11797578, … |
| maximal normal subgroup of | #11771649, #11771668, #11797578, … |
| maximal quotient of | D8×#622, #11777188, #11777231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5661);