Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #444 |
239 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 68 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=d,b^2=d,c^2=e,d^2=f,e^2=f,c^a=cf,h^a=h^2,c^b=ce,e^b=ef,g^b=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | #11797920, #11797929, #11797932, … |
| maximal normal subgroup of | #11797920, #11797929, #11797932, … |
| maximal quotient of | #11777291, #11777325, #11777358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2800);