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×Q16 ⋊ C4 |
| Sylow | C32 ⋊ #441 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=f,e^2=f,c^a=cf,g^a=gh,h^a=gh^2,c^b=ce,e^b=ef,e^c=ef,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11797918, #11797919, C2×#10593786, … |
| maximal normal subgroup of | #11797918, #11797919, C2×#10593786, … |
| maximal quotient of | #11777312, #11777313, #11777314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5668);