Finite Group DatabasebetaFinite Group Databasebeta| order | 2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C127 ⋊ C2 |
| Sylow | C127 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D127 |
| commutator, cosocle | C4×C127 | C22 |
| Frattini | C4 | C2×D127 |
| Fitting | D4×C127 | C2 |
| socle | C2×C127 | D4 |
| hypercenter | D4 | D127 |
| hypocenter | C127 | D8 |
| LCS | G ▷ C4×C127 ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 135 |
| transitive degree | μt(G) = 1016 |
Polycyclic presentation:
2^4,127|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^126322 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D127, C2×#14523233, #16861229, … |
| maximal normal subgroup of | D8×D127, C2×#14523233, #16861229, … |
| maximal quotient of | #16861129, #16861130, #16861142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2032, 25);