Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #385 |
702 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 223 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|a^2=f,c^2=d,b^a=be,c^a=cf,g^a=g^2,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #11771493, #11787057, #11787060, … |
| maximal normal subgroup of | #11771493, #11787057, #11787060, … |
| maximal quotient of | #11773157, #11773226, #11773294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4791);