Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #529 |
515 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=f,d^a=de,h^a=h^2,d^b=df,g^b=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11861690, #11861717, #11861737, … |
| maximal normal subgroup of | #11861690, #11861717, #11861737, … |
| maximal quotient of | #11801156, #11801523, #11801526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6815);