Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C31×C4⋊Q8 ⋊ C2 |
| Sylow | C31 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×C4⋊Q8 | C2 |
| prime radical | C22×D31 | C23 |
| hypercenter | C4⋊Q8 | D31 |
| hypocenter | C31 | #541 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=e,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^30,g^c=g^30232 conjugacy classes — view the full character table.
| maximal subgroup of | #16855922, #16855924, #16855961, … |
| maximal normal subgroup of | #16855922, #16855924, #16855961, … |
| maximal quotient of | #16848319, #16848356, #16848396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1160);