Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C31 ⋊ C2 |
| Sylow | C31 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D31 |
| commutator, socle | C2×C31 | C22×C4 |
| Fitting | M16×C31 | C2 |
| prime radical | #92495 | C2 |
| cosocle | C4×C31 | C23 |
| hypercenter | M16 | D31 |
| hypocenter | C31 | #131 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|c^2=d,d^2=e,b^a=be,f^a=f^30,c^b=ce170 conjugacy classes — view the full character table.
| maximal subgroup of | #14521163, #14521165, #14521168, … |
| maximal normal subgroup of | #14521163, #14521165, #14521168, … |
| maximal quotient of | #14521006, #14521007, #14521014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 102);