Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C43 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D43 |
| commutator, socle | C2×C43 | C2×C8 |
| Fitting | C2×C8×C43 | C2 |
| prime radical | C22×C43 | C8 |
| cosocle | C8×C43 | C22 |
| hypercenter | C2×C8 | D43 |
| hypocenter | C43 | M32 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^42356 conjugacy classes — view the full character table.
| maximal subgroup of | #14582676, #14582677, #14582680, … |
| maximal normal subgroup of | #14582676, #14582677, #14582680, … |
| maximal quotient of | #14582675, C22⋊(C43⋊C16), C4⋊(C43⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 86);