Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C23×C64 ⋊ C2 |
| Sylow | C23 ⋊ #7537 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D736 |
| commutator | C23×C32 | C2×C4 |
| Frattini | C2×C32 | C2×D23 |
| Fitting | C2×C23×C64 | C2 |
| socle | C22×C23 | D32 |
| hypercenter | C2×C64 | D23 |
| hypocenter | C23 | #7537 |
| LCS | G ▷ C23×C32 ▷ C16×C23 ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64 | |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=d,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^22,c^b=ce,e^b=ef,f^b=fg,g^b=gh,i^b=i^221478 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57447);