Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C251 ⋊ C2 |
| Sylow | C251 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D251 |
| commutator, socle | C2×C251 | C22×C4 |
| Fitting | M16×C251 | C2 |
| hypercenter | M16 | D251 |
| hypocenter | C251 | #131 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,251|a^2=d,d^2=e,f^a=f^250,c^b=ce,f^c=f^2501270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631801, #30631803, #30631806, … |
| maximal normal subgroup of | #30631801, #30631803, #30631806, … |
| maximal quotient of | #30631644, #30631645, #30631652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 154);