Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #328 |
142 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,d^a=def,g^a=g^2,c^b=cf,g^b=h,h^b=g,g^c=g^2,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590034, #11774968, #11775004, … |
| maximal normal subgroup of | C2×#10590034, #11774968, #11775004, … |
| maximal quotient of | #11770680, #11770694, #11771056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1916);