Finite Group DatabasebetaFinite Group Databasebeta| order | 8032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16860800 |
| Sylow | C251 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D251 |
| commutator | C4×C251 | C23 |
| Frattini | C4 | C22×D251 |
| Fitting | C2×Q8×C251 | C2 |
| socle | C22×C251 | D4 |
| hypercenter | C2×Q8 | D251 |
| hypocenter | C251 | C2×Q16 |
| LCS | G ▷ C4×C251 ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
60 conjugacy classes of subgroups.
1264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30631779, C4×#16860800, #30631791, … |
| maximal normal subgroup of | #30631779, C4×#16860800, #30631791, … |
| maximal quotient of | C2×#22548638, C2×#22548639, C2×#22548648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8032, 163);