Finite Group DatabasebetaFinite Group Databasebeta| order | 7984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D499 |
| Fitting | C8×C499 ⋊ C2 |
| derived, Sylow | C499 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D499 |
| commutator, hypocenter | C499 | C2×C8 |
| Frattini | C4 | C2×D499 |
| Fitting | C8×C499 | C2 |
| socle | C2×C499 | C2×C4 |
| LCS | G ▷ C499 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
2008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D499, #30630290, C2×C8×D499, … |
| maximal normal subgroup of | C16×D499, #30630290, C2×C8×D499, … |
| maximal quotient of | C8×Dic499, (C2×D499)⋊C8, Dic499⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7984, 21);