Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C23×C32 ⋊ C2 |
| Sylow | C23 ⋊ SD64 |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^22,c^b=cd,d^b=de,e^b=ef,g^b=g^22371 conjugacy classes — view the full character table.
| maximal subgroup of | D23×SD64, C2×#13092256, #15675705, … |
| maximal normal subgroup of | D23×SD64, C2×#13092256, #15675705, … |
| maximal quotient of | #15671576, #15671579, #15671599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 388);