Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C31×M32 ⋊ C2 |
| Sylow | C31 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D31 |
| commutator, socle | C2×C31 | C22×C8 |
| Fitting | C31×M32 | C2 |
| prime radical | #92495 | C4 |
| cosocle | C8×C31 | C23 |
| hypercenter | M32 | D31 |
| hypocenter | C31 | #504 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=d,d^2=e,e^2=f,g^a=g^30,c^b=cf,g^c=g^30340 conjugacy classes — view the full character table.
| maximal subgroup of | #16847545, #16847547, #16847550, … |
| maximal normal subgroup of | #16847545, #16847547, #16847550, … |
| maximal quotient of | #16847309, #16847310, #16847323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 967);