Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| Fitting | C32×#97 ⋊ C2 |
| Sylow | C32 ⋊ #489 |
300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 95 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,c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^2,c^b=cf96 conjugacy classes — view the full character table.
| maximal subgroup of | #11780566, #11780569, #11780582, … |
| maximal normal subgroup of | #11780566, #11780569, #11780582, … |
| maximal quotient of | #11786068, #11789841, #11789887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4295);