Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C31×#131 ⋊ C2 |
| Sylow | C31 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D124 |
| commutator, cosocle | C4×C31 | C24 |
| Frattini | C4 | C23×D31 |
| Fitting | C31×#131 | C2 |
| socle | C2×C31 | C22×D4 |
| hypercenter | #131 | D31 |
| hypocenter | C31 | #578 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^30,e^b=ef,g^b=g^30,d^c=df322 conjugacy classes — view the full character table.
| maximal subgroup of | #16847673, #16847677, #16847687, … |
| maximal normal subgroup of | #16847673, #16847677, #16847687, … |
| maximal quotient of | #16854245, #16854311, #16854556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1366);