Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C23⋊C64) |
| Sylow | C23 ⋊ C4⋊C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C32 | C2×D23 |
| commutator | C2×C23 | C2×C64 |
| Fitting | C4×C23×C32 | C2 |
| socle | C22×C23 | C2×C32 |
| hypercenter | C4×C32 | D23 |
| hypocenter | C23 | C4⋊C64 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C32 ◁ C4×C32 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^221568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57464);