Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ #520 |
441 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=f,d^2=e,g^3=h,c^a=cf,g^a=g^2h^2,h^a=h^2,c^b=cf,d^b=df114 conjugacy classes — view the full character table.
| maximal subgroup of | #11860454, #11860466, #11860556, … |
| maximal normal subgroup of | #11860454, #11860466, #11860556, … |
| maximal quotient of | #11800866, #11800869, #11800899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1530);