Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #349 |
105 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 105 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|b^2=d,d^2=e,e^2=f,b^a=bc,d^a=df,g^a=g^2,c^b=cf,g^b=h,h^b=g,g^c=g^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590013, #11796043, #11796065, … |
| maximal normal subgroup of | C2×#10590013, #11796043, #11796065, … |
| maximal quotient of | #11771346, #11771446, #11771560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1895);