Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D8×C31 ⋊ C2 |
| Sylow | C31 ⋊ #576 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D31 |
| commutator, cosocle | C4×C31 | C24 |
| Frattini | C4 | C23×D31 |
| Fitting | C2×D8×C31 | C2 |
| socle | C2×C31 | C22×D4 |
| hypercenter | C2×D8 | D31 |
| hypocenter | C31 | #576 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^d=g^30232 conjugacy classes — view the full character table.
| maximal subgroup of | #16847667, #16847671, #16847681, … |
| maximal normal subgroup of | #16847667, #16847671, #16847681, … |
| maximal quotient of | #16854232, #16854307, #16854536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1350);