Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D31 |
| Fitting | D8×C31 ⋊ C2 |
| Sylow | C31 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D31 |
| commutator, cosocle | C4×C31 | C23 |
| Frattini | C4 | C22×D31 |
| Fitting | D8×C31 | C2 |
| socle | C2×C31 | C2×D4 |
| hypercenter | D8 | D31 |
| hypocenter | C31 | C2×D8 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D31, SD32×D31, #14521483, … |
| maximal normal subgroup of | D16×D31, SD32×D31, #14521483, … |
| maximal quotient of | #102×D31, #107×D31, #14521129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 105);