Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×#106 ⋊ C2 |
| Sylow | C23 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^c=g^22176 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#428, C2×#13092456, #15681984, … |
| maximal normal subgroup of | D23×#428, C2×#13092456, #15681984, … |
| maximal quotient of | #15672146, #15672161, #15672179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 588);