Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C31 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D31 |
| commutator, socle, prime radical | C22×C31 | C22×C4 |
| Fitting | C4×Q8×C31 | C2 |
| cosocle | C2×C4×C31 | C23 |
| hypercenter | C4×Q8 | D31 |
| hypocenter | C31 | #446 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^6,31|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^30,g^c=g^30328 conjugacy classes — view the full character table.
| maximal subgroup of | #16844548, #16844550, #16844562, … |
| maximal normal subgroup of | #16844548, #16844550, #16844562, … |
| maximal quotient of | #16845580, #16845586, #16846270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 680);