Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #510 |
176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=f,c^2=de,d^2=e,e^2=f,c^a=cf,h^a=h^2,c^b=cd,d^b=def,e^b=ef,g^b=g^263 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4915, #11899597, D3×#4909, … |
| maximal normal subgroup of | D3×#4915, #11899597, D3×#4909, … |
| maximal quotient of | #11796692, #11796745, #11797229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2121);