Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D31)⋊C4 |
| Fitting | C22⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|c^2=d,b^a=be,f^a=f^30,c^b=ce170 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D31, C2×(C22⋊D31)⋊C4, C4×#92497, … |
| maximal normal subgroup of | C4×D4×D31, C2×(C22⋊D31)⋊C4, C4×#92497, … |
| maximal quotient of | #14520896, C22⋊C4×Dic31, #14520900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 76);