Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×C4×D4 |
918 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|d^2=e,c^a=cf,h^a=h^2,c^b=cf,g^b=g^2,d^c=df90 conjugacy classes — view the full character table.
| maximal subgroup of | #11806169, #11806321, #11806522, … |
| maximal normal subgroup of | #11806169, #11806321, #11806522, … |
| maximal quotient of | #11800698, C22⋊C4×#624, #11800733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6137);