Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #495 |
298 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 298 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) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=f,c^2=df,d^2=f,b^a=bef,h^a=h^2,c^b=cd,d^b=df,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11798985, #11798992, #11798994, … |
| maximal normal subgroup of | #11798985, #11798992, #11798994, … |
| maximal quotient of | #11782449, #11782483, #11782515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2747);