Finite Group DatabasebetaFinite Group Databasebeta| order | 8048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D503)⋊C4 |
| Fitting | C2×C4×C503 ⋊ C2 |
| Sylow | C503 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D503 |
| commutator | C2×C503 | C2×C4 |
| Fitting | C2×C4×C503 | C2 |
| socle | C22×C503 | C22 |
| hypercenter | C2×C4 | D503 |
| hypocenter | C503 | C22⋊C4 |
| LCS | G ▷ C2×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,503|a^2=d,b^a=bc,e^b=e^5022018 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D503, C2×(C2×D503)⋊C4, #30632821, … |
| maximal normal subgroup of | C22⋊C4×D503, C2×(C2×D503)⋊C4, #30632821, … |
| maximal quotient of | C503⋊#95, (C2×D503)⋊C8, #30632778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8048, 17);