Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C23 ⋊ C2 |
| Sylow | C23 ⋊ #448 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^22,d^b=df239 conjugacy classes — view the full character table.
| maximal subgroup of | #15672347, #15672348, #15672358, … |
| maximal normal subgroup of | #15672347, #15672348, #15672358, … |
| maximal quotient of | #15672320, #15672337, #15672388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 688);