Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×#97 ⋊ C2 |
| Sylow | C23 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^22,d^b=df,g^b=g^22242 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#440, C2×#13092519, #15682192, … |
| maximal normal subgroup of | D23×#440, C2×#13092519, #15682192, … |
| maximal quotient of | #15672211, #15672256, #15672277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 651);