Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #336 |
145 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=cd,d^2=f,b^a=bce,g^a=g^2h^2,h^a=g^2h,g^b=gh^2,h^b=g^2h^2,g^c=g^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11770663, #11770682, C2×#10590090, … |
| maximal normal subgroup of | #11770663, #11770682, C2×#10590090, … |
| maximal quotient of | #11770703, #11770717, #11770731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1972);