Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C22×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ #466 |
402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,h^a=h^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #11771848, #11771854, #11771859, … |
| maximal normal subgroup of | #11771848, #11771854, #11771859, … |
| maximal quotient of | #11780883, #11780915, #11781108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4696);