Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C43⋊#95 |
| Sylow | C43 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D43 |
| commutator | C2×C43 | C42 |
| Fitting | C22×C4×C43 | C2 |
| socle, prime radical, cosocle | C23×C43 | C22 |
| hypercenter | C22×C4 | D43 |
| hypocenter | C43 | #95 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1376 |
Polycyclic presentation:
2^5,43|a^2=d,b^2=e,b^a=bc,f^b=f^42356 conjugacy classes — view the full character table.
| maximal subgroup of | #14582633, #14582634, #14582636, … |
| maximal normal subgroup of | #14582633, #14582634, #14582636, … |
| maximal quotient of | #14582653, #14582654, #14582655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 53);