Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ C4×Q16 |
255 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 74 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|a^2=e,b^2=f,c^2=e,d^2=f,c^a=cd,d^a=df,h^a=h^2,c^b=cd,d^b=df,g^b=g^2,d^c=df66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4790, C4×#63944, C2×#10590482, … |
| maximal normal subgroup of | D3×#4790, C4×#63944, C2×#10590482, … |
| maximal quotient of | #11777233, #11777535, #11777550, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2364);