Finite Group DatabasebetaFinite Group Databasebeta| order | 7984 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C499⋊C16 |
| derived, Sylow | C499 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D499 |
| commutator, hypocenter | C499 | C16 |
| Fitting | C8×C499 | C2 |
| socle | C2×C499 | C8 |
| LCS | G ▷ C499 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,499|a^2=b,b^2=c,c^2=d,e^a=e^4982008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D499, C2×C499⋊C16, #30630290, … |
| maximal normal subgroup of | C16×D499, C2×C499⋊C16, #30630290, … |
| maximal quotient of | C499⋊C32, C2×C499⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7984, 15);