Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C251 ⋊ C2 |
| Sylow | C251 ⋊ SD32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16860795 |
| commutator | C8×C251 | C22 |
| Frattini | C8 | C2×D251 |
| Fitting | Q16×C251 | C2 |
| socle | C2×C251 | D8 |
| hypercenter | Q16 | D251 |
| hypocenter | C251 | SD32 |
| LCS | G ▷ C8×C251 ▷ C4×C251 ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^250886 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D251, C2×#22548658, #30632117, … |
| maximal normal subgroup of | SD32×D251, C2×#22548658, #30632117, … |
| maximal quotient of | #30631487, #30631491, #30631514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 89);