Finite Group DatabasebetaFinite Group Databasebeta| order | 8048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C503⋊C8 |
| unambiguous semidirect product | (C2×C503)⋊C8 |
| derived, Sylow | C503 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D503 |
| commutator, hypocenter | C503 | C2×C8 |
| Frattini | C4 | C2×D503 |
| Fitting | C2×C4×C503 | C2 |
| socle | C22×C503 | C4 |
| LCS | G ▷ C503 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
2024 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic503, C4×C503⋊C8, #30632774, … |
| maximal normal subgroup of | C8×Dic503, C4×C503⋊C8, #30632774, … |
| maximal quotient of | C4×C503⋊C8, C22⋊(C503⋊C8), C4⋊(C503⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8048, 22);