Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C31 ⋊ C2 |
| Sylow | C31 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|b^2=e,c^2=e,d^2=e,c^a=ce,f^a=f^30,c^b=cd,d^b=de,d^c=de116 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D31, C2×#11758495, #14521846, … |
| maximal normal subgroup of | #137×D31, C2×#11758495, #14521846, … |
| maximal quotient of | #14521049, #14521056, #14521090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 113);