Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C32×C4 ⋊ C8 |
| Sylow | C32 ⋊ #336 |
145 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=f,b^a=be,g^a=g^2h^2,h^a=g^2,g^c=g^2h,h^c=gh,g^f=g^2,h^f=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11770661, #11770663, #11770678, … |
| maximal normal subgroup of | #11770661, #11770663, #11770678, … |
| maximal quotient of | #11770701, #11770714, #11770728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5149);