Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C23×#117 ⋊ C2 |
| Sylow | C23 ⋊ #410 |
158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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,c^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^22242 conjugacy classes — view the full character table.
| maximal subgroup of | #15673196, #15673198, #15673359, … |
| maximal normal subgroup of | #15673196, #15673198, #15673359, … |
| maximal quotient of | #15671709, #15671717, #15671720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 522);