Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #509 |
193 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 193 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|d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,h^a=h^2,c^b=cf,d^b=de,e^b=ef,g^b=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11797968, #11797974, #11797976, … |
| maximal normal subgroup of | #11797968, #11797974, #11797976, … |
| maximal quotient of | #11796689, #11796718, #11797233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2512);