Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C43 ⋊ C2 |
| Sylow | C43 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D43 |
| commutator, socle | C2×C43 | C22×C4 |
| Fitting | M16×C43 | C2 |
| prime radical | #10621898 | C2 |
| cosocle | C4×C43 | C23 |
| hypercenter | M16 | D43 |
| hypocenter | C43 | #131 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^5,43|a^2=d,d^2=e,f^a=f^42,c^b=ce,f^c=f^42230 conjugacy classes — view the full character table.
| maximal subgroup of | #14583013, #14583015, #14583018, … |
| maximal normal subgroup of | #14583013, #14583015, #14583018, … |
| maximal quotient of | #14582856, #14582857, #14582864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 154);