Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Sylow | C23 ⋊ #7554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C25 | C22×D23 |
| commutator | C22×C23 | C43 |
| Fitting | C23×C42×C23 | C2 |
| socle | C25×C23 | C23 |
| hypercenter | C23×C42 | D23 |
| hypocenter | C23 | #7554 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C25 ◁ C23×C42 | |
3158 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=f,b^2=g,c^2=h,b^a=bd,c^a=ce,i^a=i^221520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57488);