Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D47)⋊C4 |
| Fitting | C22⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^5,47|a^2=e,c^2=e,b^a=bd,f^c=f^46250 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D47, C2×(C22⋊D47)⋊C4, C4×#10625352, … |
| maximal normal subgroup of | C4×D4×D47, C2×(C22⋊D47)⋊C4, C4×#10625352, … |
| maximal quotient of | #15688970, C22⋊C4×Dic47, #15688974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 106);