Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #359 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=f,d^2=ef,e^2=f,g^3=h^2,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,d^b=de,e^b=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#359, C2×#10588244, #11796781, … |
| maximal normal subgroup of | D9×#359, C2×#10588244, #11796781, … |
| maximal quotient of | #11771566, #11771584, #11771884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 126);