Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C23 ⋊ C2 |
| Sylow | C23 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^22,c^b=ce,g^b=g^22380 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D4⋊C8, C2×#13092146, #15671778, … |
| maximal normal subgroup of | D23×D4⋊C8, C2×#13092146, #15671778, … |
| maximal quotient of | #15671217, #15671219, #15671237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 278);