Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C31⋊C8) |
| Sylow | C31 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D31 |
| commutator | C2×C31 | C2×C8 |
| Fitting | C42×C31 | C2 |
| socle, prime radical | C22×C31 | C2×C4 |
| cosocle | C2×C4×C31 | C22 |
| hypercenter | C42 | D31 |
| hypocenter | C31 | C4⋊C8 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^5,31|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^30260 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊(C31⋊C8), #14520778, Q8⋊(C31⋊C8), … |
| maximal normal subgroup of | D4⋊(C31⋊C8), #14520778, Q8⋊(C31⋊C8), … |
| maximal quotient of | #14520800, #14520802, #14520804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 10);