Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C32 ⋊ Q64 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^2,c^b=cd,d^b=de,e^b=ef,g^b=h,h^b=g,g^c=g^2,h^c=h^233 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590026, #11800549, #11800578, … |
| maximal normal subgroup of | C2×#10590026, #11800549, #11800578, … |
| maximal quotient of | #11772936, #11773042, C2×#10590026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1908);