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 |
250 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 80 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=d,b^2=df,c^2=ef,e^2=f,h^a=h^2,c^b=ce,e^b=ef,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | #11797670, #11797679, #11797682, … |
| maximal normal subgroup of | #11797670, #11797679, #11797682, … |
| maximal quotient of | #11777242, #11777552, #11777859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2689);