Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C23 ⋊ #577 |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|a^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^22,d^c=df,g^c=g^22,g^d=g^22143 conjugacy classes — view the full character table.
| maximal subgroup of | #15685158, #15685160, #15685169, … |
| maximal normal subgroup of | #15685158, #15685160, #15685169, … |
| maximal quotient of | #15681922, #15681928, #15681991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1359);