Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ C22 |
| Sylow | C32 ⋊ C2×AGL(1,ℤ/8) |
714 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^2|c^2=f,e^2=f,d^a=de,e^a=ef,h^a=h^2,d^b=de,e^b=ef,g^b=g^2,d^c=df,e^d=ef54 conjugacy classes — view the full character table.
| maximal subgroup of | #11788500, #11788502, #11792075, … |
| maximal normal subgroup of | #11788500, #11788502, #11792075, … |
| maximal quotient of | #11857833, #11857908, #11858472, … |
| holomorph of | C3⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6982);