Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #508 |
199 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 56 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=de,c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,h^a=h^2,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11797849, #11797850, #11797855, … |
| maximal normal subgroup of | #11797849, #11797850, #11797855, … |
| maximal quotient of | #11796654, #11796655, #11797203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2514);