Finite Group DatabasebetaFinite Group Databasebeta| order | 7984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic499 |
| derived, Sylow | C499 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D499 |
| commutator, hypocenter | C499 | C22×C4 |
| Frattini | C2 | C22×D499 |
| Fitting, socle | C23×C499 | C2 |
| LCS | G ▷ C499 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
2008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C499⋊#95, C2×C4×Dic499, C2×(C2×D499)⋊C4, … |
| maximal normal subgroup of | C499⋊#95, C2×C4×Dic499, C2×(C2×D499)⋊C4, … |
| maximal quotient of | C2×C4×Dic499, C2×C22⋊Dic499, C2×C4⋊Dic499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7984, 33);