Finite Group DatabasebetaFinite Group Databasebeta| order | 8048 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C503⋊C16 |
| derived, Sylow | C503 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D503 |
| commutator, hypocenter | C503 | C16 |
| Fitting | C8×C503 | C2 |
| socle | C2×C503 | C8 |
| LCS | G ▷ C503 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,503|a^2=b,b^2=c,c^2=d,e^a=e^5022024 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D503, C2×C503⋊C16, #30632803, … |
| maximal normal subgroup of | C16×D503, C2×C503⋊C16, #30632803, … |
| maximal quotient of | C503⋊C32, C2×C503⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8048, 15);