Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#131 |
430 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=e,c^2=f,e^2=f,g^a=gh,h^a=gh^2,d^b=df,g^e=g^2,h^e=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11784080, #11784129, #11785564, … |
| maximal normal subgroup of | #11784080, #11784129, #11785564, … |
| maximal quotient of | #11857190, C4×#64287, C4×#64289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8529);