Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^22,c^b=ce,e^b=ef176 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#359, C2×#13092224, #15675123, … |
| maximal normal subgroup of | D23×#359, C2×#13092224, #15675123, … |
| maximal quotient of | #15671358, #15671361, #15671412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 356);