Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C251 ⋊ C2 |
| Sylow | C251 ⋊ #137 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D251 |
| commutator | C4×C251 | C23 |
| Frattini | C4 | C22×D251 |
| Fitting | Q16×C251 | C2 |
| socle | C2×C251 | C2×D4 |
| hypercenter | Q16 | D251 |
| hypocenter | C251 | #137 |
| LCS | G ▷ C4×C251 ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^250,d^b=de,f^c=f^250886 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D251, C2×#22548747, #30632484, … |
| maximal normal subgroup of | #137×D251, C2×#22548747, #30632484, … |
| maximal quotient of | #30631687, #30631694, #30631728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 178);