Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D31 |
| commutator, socle, cosocle | C22×C31 | C23 |
| Fitting | C22⋊C4×C31 | C2 |
| prime radical | C2×C22⋊D31 | C2 |
| hypercenter | C22⋊C4 | D31 |
| hypocenter | C31 | #123 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|c^2=de,b^a=be,c^a=cd,f^a=f^30,c^b=ce164 conjugacy classes — view the full character table.
| maximal subgroup of | #14521240, #123×D31, C2×#11758463, … |
| maximal normal subgroup of | #14521240, #123×D31, C2×#11758463, … |
| maximal quotient of | #14520910, #14520924, #14520926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 81);