Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C23×C4⋊Q8 ⋊ C2 |
| Sylow | C23 ⋊ #489 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^22,c^b=cf,g^b=g^22,g^c=g^22170 conjugacy classes — view the full character table.
| maximal subgroup of | #15672701, #15672702, #15672711, … |
| maximal normal subgroup of | #15672701, #15672702, #15672711, … |
| maximal quotient of | #15673532, #15674086, #15674093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 911);