Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #7540 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15671575 |
| commutator | C23×C32 | C2×C4 |
| Frattini | C2×C32 | C2×D23 |
| Fitting | C23×#2262 | C2 |
| socle | C2×C23 | #1415 |
| hypercenter | #2262 | D23 |
| hypocenter | C23 | #7540 |
| LCS | G ▷ C23×C32 ▷ C16×C23 ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ #2262 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,23|a^2=d,c^2=efh,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=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 57455);