Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #510 |
195 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 44 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,b^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,h^a=h^2,c^b=cdf,d^b=de,e^b=ef,g^b=g^2,d^c=de,e^c=ef45 conjugacy classes — view the full character table.
| maximal subgroup of | #11798320, #11798460, #11798507, … |
| maximal normal subgroup of | #11798320, #11798460, #11798507, … |
| maximal quotient of | #11796686, #11796739, #11797238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2912);