Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C31 ⋊ C2 |
| Sylow | C31 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D31 |
| commutator, socle, cosocle | C23×C31 | C23 |
| Fitting | C22×Q8×C31 | C2 |
| prime radical | C23×D31 | C22 |
| hypercenter | C22×Q8 | D31 |
| hypocenter | C31 | #393 |
| LCS | G ▷ C23×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^30322 conjugacy classes — view the full character table.
| maximal subgroup of | #16844661, #16844666, #16844688, … |
| maximal normal subgroup of | #16844661, #16844666, #16844688, … |
| maximal quotient of | #16843953, #16843970, #16843982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 460);