Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #518 |
714 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 240 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|b^2=e,d^2=f,d^a=df,h^a=h^2,c^b=cf,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | #11785925, #11785926, #11786581, … |
| maximal normal subgroup of | #11785925, #11785926, #11786581, … |
| maximal quotient of | #11800861, #11800894, #11800920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6864);