Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #360 |
87 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,d^2=e,e^2=f,g^3=h^2,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,c^b=cf,d^b=def,e^b=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#360, C2×#10588243, #11796841, … |
| maximal normal subgroup of | D9×#360, C2×#10588243, #11796841, … |
| maximal quotient of | #11771602, #11771620, #11771850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 125);