Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C23×#103 ⋊ C2 |
| Sylow | C23 ⋊ #419 |
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^c=g^22176 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#419, C2×#13092424, #15681912, … |
| maximal normal subgroup of | D23×#419, C2×#13092424, #15681912, … |
| maximal quotient of | #15671790, #15671816, #15671842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 556);