Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #336 |
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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,d^2=f,b^a=bc,g^a=g^2,g^b=h,h^b=g,g^c=g^2,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590043, #11783093, #11783121, … |
| maximal normal subgroup of | C2×#10590043, #11783093, #11783121, … |
| maximal quotient of | #11770702, #11770716, #11770730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1925);