Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C23×M128 ⋊ C2 |
| Sylow | C23 ⋊ #7514 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C22⋊D23 |
| commutator | C4×C23 | C2×C32 |
| Frattini | C2×C32 | C2×D23 |
| Fitting | C23×M128 | C2 |
| socle | C2×C23 | C22⋊C32 |
| hypercenter | M128 | D23 |
| hypocenter | C23 | #7514 |
| LCS | G ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C32 ◁ C2×C32 ◁ M128 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=d,c^2=h,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^22,c^b=ch,d^b=dh,i^b=i^22992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57382);