Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×SD32 ⋊ C2 |
| Sylow | C32 ⋊ #510 |
246 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 63 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=f,d^2=ef,e^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=cd,d^b=de,e^b=ef,d^c=de,e^c=ef60 conjugacy classes — view the full character table.
| maximal subgroup of | #11797918, C3⋊D3×#510, C2×#10592614, … |
| maximal normal subgroup of | #11797918, C3⋊D3×#510, C2×#10592614, … |
| maximal quotient of | #11796667, #11796726, #11797217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4496);