Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C31 ⋊ Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11758414 |
| commutator, cosocle | C16×C31 | C22 |
| Frattini | C16 | C2×D31 |
| Fitting | C31×Q32 | C2 |
| socle, prime radical | C2×C31 | D16 |
| hypercenter | Q32 | D31 |
| hypocenter | C31 | Q64 |
| LCS | G ▷ C16×C31 ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^6,31|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^30184 conjugacy classes — view the full character table.
| maximal subgroup of | D31×Q64, C2×#14520889, #16848018, … |
| maximal normal subgroup of | D31×Q64, C2×#14520889, #16848018, … |
| maximal quotient of | #16843891, #16843892, #16843910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 389);