Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #352 |
102 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^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=ce,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#352, C2×#10588216, #11796191, … |
| maximal normal subgroup of | D9×#352, C2×#10588216, #11796191, … |
| maximal quotient of | #11771375, #11771486, #11771799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 98);