Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #444 |
228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 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|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,h^a=h^2,c^b=cf,e^b=ef,g^b=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | #11797941, #11797987, D3×#5145, … |
| maximal normal subgroup of | #11797941, #11797987, D3×#5145, … |
| maximal quotient of | #11777281, #11777322, #11777355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2804);