Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #102 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D1004 |
| commutator | C4×C251 | C2×C4 |
| Frattini | C2×C4 | C2×D251 |
| Fitting | C2×C8×C251 | C2 |
| socle | C22×C251 | D4 |
| hypercenter | C2×C8 | D251 |
| hypocenter | C251 | #102 |
| LCS | G ▷ C4×C251 ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^250,c^b=ce,f^b=f^2502014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D251, C2×#22548637, #30631682, … |
| maximal normal subgroup of | #102×D251, C2×#22548637, #30631682, … |
| maximal quotient of | #30631416, #30631422, #30631430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 68);