Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×H(5,𝔽2) ⋊ C2 |
| Sylow | C23 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 184 |
Polycyclic presentation:
2^6,23|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^22,d^b=df,e^b=ef,d^c=df203 conjugacy classes — view the full character table.
| maximal subgroup of | #15675379, #15675391, #15675401, … |
| maximal normal subgroup of | #15675379, #15675391, #15675401, … |
| maximal quotient of | #15672315, #15672320, #15672343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 717);