Finite Group DatabasebetaFinite Group Databasebeta| order | 7984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C499 ⋊ C2 |
| Sylow | C499 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D499 |
| commutator, socle | C2×C499 | C23 |
| Fitting | Q8×C499 | C2 |
| hypercenter | Q8 | D499 |
| hypocenter | C499 | #41 |
| LCS | G ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,499|c^2=d,b^a=bd,e^a=e^498,e^b=e^498,e^c=e^4981255 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30630372, #30630374, #30630378, … |
| maximal normal subgroup of | #30630372, #30630374, #30630378, … |
| maximal quotient of | #30630309, #30630313, Q8×Dic499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7984, 41);