Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C32×C16 ⋊ C22 |
| Sylow | C32 ⋊ C2×SD32 |
194 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 46 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|c^2=de,d^2=e,e^2=f,c^a=cd,d^a=def,e^a=ef,h^a=h^2,c^b=cd,d^b=def,e^b=ef,g^b=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11799262, #11799369, #11799478, … |
| maximal normal subgroup of | #11799262, #11799369, #11799478, … |
| maximal quotient of | #11796602, #11796628, #11797179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2117);