Finite Group DatabasebetaFinite Group Databasebeta| order | 2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C127 ⋊ C2 |
| Sylow | C127 ⋊ SD16 |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 135 |
| transitive degree | μt(G) = 1016 |
Polycyclic presentation:
2^4,127|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^126,c^b=cd,e^b=e^126511 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D127, C2×#14523237, #16861230, … |
| maximal normal subgroup of | SD16×D127, C2×#14523237, #16861230, … |
| maximal quotient of | #16861131, #16861134, #16861141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2032, 29);