Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #357 |
146 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=c,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,h^a=h^2,d^b=de,e^b=ef,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4491, D3×#4562, C2×#10589114, … |
| maximal normal subgroup of | D3×#4491, D3×#4562, C2×#10589114, … |
| maximal quotient of | #11771576, #11771860, #11772069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 996);