Finite Group DatabasebetaFinite Group Databasebeta| order | 2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D127 |
| commutator, socle, cosocle | C2×C127 | C23 |
| Fitting | Q8×C127 | C2 |
| hypercenter | Q8 | D127 |
| hypocenter | C127 | #41 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1016 |
Polycyclic presentation:
2^4,127|c^2=d,b^a=bd,e^a=e^126,e^b=e^126,e^c=e^126325 conjugacy classes — view the full character table.
| maximal subgroup of | #16861230, #16861232, #16861236, … |
| maximal normal subgroup of | #16861230, #16861232, #16861236, … |
| maximal quotient of | #16861167, #16861171, Q8×Dic127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2032, 41);