Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C31×H(5,𝔽2) ⋊ C2 |
| Sylow | C31 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D31 |
| commutator, socle, cosocle | C2×C31 | C25 |
| Fitting | C31×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D31 |
| hypocenter | C31 | #585 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|e^2=f,b^a=bf,d^a=df,c^b=cf,g^e=g^30289 conjugacy classes — view the full character table.
| maximal subgroup of | #16855056, #16855061, #16855079, … |
| maximal normal subgroup of | #16855056, #16855061, #16855079, … |
| maximal quotient of | #16858909, #16858911, #16858915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1384);