Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C23 ⋊ M256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C64 | C2×D23 |
| commutator, socle | C2×C23 | C2×C64 |
| Fitting | C2×C23×C64 | C2 |
| hypercenter | C2×C64 | D23 |
| hypocenter | C23 | M256 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C64 ◁ C2×C64 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,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, 57479);