Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C31 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D31 |
| commutator, socle, prime radical, cosocle | C22×C31 | C23 |
| Fitting | C42×C31 | C2 |
| hypercenter | C42 | D31 |
| hypocenter | C31 | #125 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C42 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^5,31|a^2=e,b^2=d,c^2=e,b^a=be,c^a=cd,f^a=f^30254 conjugacy classes — view the full character table.
| maximal subgroup of | #14520790, #14521349, #14521350, … |
| maximal normal subgroup of | #14520790, #14521349, #14521350, … |
| maximal quotient of | #14520915, #14520933, #14520947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 65);