Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C22⋊C8 ⋊ C2 |
| Sylow | C23 ⋊ #327 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|a^2=d,c^2=f,b^a=bc,c^a=ce,g^a=g^22,c^b=cf,d^b=def,g^b=g^22239 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#327, C2×#13092152, #15671882, … |
| maximal normal subgroup of | D23×#327, C2×#13092152, #15671882, … |
| maximal quotient of | #15671217, #15671219, #15671277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 284);