Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ C4×#41 |
658 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,c^2=e,h^a=h^2,d^b=def,g^b=g^2,d^c=def90 conjugacy classes — view the full character table.
| maximal subgroup of | #11788598, C4×D3×#237, #11899966, … |
| maximal normal subgroup of | #11788598, C4×D3×#237, #11899966, … |
| maximal quotient of | #11800772, #11800775, #11800811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5932);