Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #497 |
286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 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=f,b^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,h^a=h^2,c^b=cdef,d^b=df,g^b=g^2,d^c=df54 conjugacy classes — view the full character table.
| maximal subgroup of | #11772823, #11780584, #11780616, … |
| maximal normal subgroup of | #11772823, #11780584, #11780616, … |
| maximal quotient of | #11782634, #11782715, #11782795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3375);