Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C23 ⋊ #7511 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C4×Dic23 |
| commutator | C4×C23 | C4×C16 |
| Frattini | C2×C32 | C2×D23 |
| Fitting | C23×M128 | C2 |
| socle | C2×C23 | #1397 |
| hypercenter | M128 | D23 |
| hypocenter | C23 | #7511 |
| LCS | G ▷ C4×C23 ▷ C23 | |
| UCS | C1 ◁ C16 ◁ M128 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bg,d^a=dh,c^b=ch,i^b=i^22968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57374);