Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#101 |
326 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 72 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=f,b^2=f,c^2=d,d^2=f,c^a=ce,d^a=df,h^a=h^2,c^b=ce,d^b=df,g^b=g^2,e^c=ef54 conjugacy classes — view the full character table.
| maximal subgroup of | #11788357, #11788407, #11788695, … |
| maximal normal subgroup of | #11788357, #11788407, #11788695, … |
| maximal quotient of | #11773738, #11773836, #11773877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2885);