Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C23 ⋊ #421 |
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^22,c^b=cf,d^b=df242 conjugacy classes — view the full character table.
| maximal subgroup of | #15673361, #15673362, #15673366, … |
| maximal normal subgroup of | #15673361, #15673362, #15673366, … |
| maximal quotient of | #15671784, #15671788, #15671792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 566);