Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^42,d^b=de,f^c=f^42158 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D43, C2×#13063357, #14583696, … |
| maximal normal subgroup of | #137×D43, C2×#13063357, #14583696, … |
| maximal quotient of | #14582899, #14582906, #14582940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 178);