Finite Group DatabasebetaFinite Group Databasebeta| order | 7984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C499 ⋊ C2 |
| Sylow | C499 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D499 |
| commutator | C4×C499 | C22 |
| Frattini | C4 | C2×D499 |
| Fitting | Q8×C499 | C2 |
| socle | C2×C499 | D4 |
| hypercenter | Q8 | D499 |
| hypocenter | C499 | SD16 |
| LCS | G ▷ C4×C499 ▷ C2×C499 ▷ C499 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,499|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^4981252 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D499, C2×#22547798, #30630371, … |
| maximal normal subgroup of | SD16×D499, C2×#22547798, #30630371, … |
| maximal quotient of | #30630271, #30630275, #30630282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7984, 27);