Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#41×C23 ⋊ C2 |
| Sylow | C23 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^b=g^22242 conjugacy classes — view the full character table.
| maximal subgroup of | #15673756, #15673757, #15673759, … |
| maximal normal subgroup of | #15673756, #15673757, #15673759, … |
| maximal quotient of | #15681914, #15681916, #15681986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1347);