Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×C4⋊Q8 ⋊ C2 |
| Sylow | C23 ⋊ #456 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^22,d^c=df170 conjugacy classes — view the full character table.
| maximal subgroup of | #15671550, #15671552, #15675418, … |
| maximal normal subgroup of | #15671550, #15671552, #15675418, … |
| maximal quotient of | #15672358, #15672365, #15672370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 731);