Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #533 |
498 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 164 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=e,c^2=f,b^a=be,d^a=df,h^a=h^2,d^b=df,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11774407, #11774537, #11774779, … |
| maximal normal subgroup of | #11774407, #11774537, #11774779, … |
| maximal quotient of | #11801229, #11801786, #11801844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6932);