Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C4⋊C8 ⋊ C2 |
| Sylow | C23 ⋊ #463 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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|b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^22,e^c=ef,g^c=g^22239 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#463, C2×#13092633, #15682851, … |
| maximal normal subgroup of | D23×#463, C2×#13092633, #15682851, … |
| maximal quotient of | #15672807, #15672821, #15672835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 765);