Finite Group DatabasebetaFinite Group Databasebeta| order | 2032 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D127 |
| Fitting | C8×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D127 |
| commutator, hypocenter | C127 | C2×C8 |
| Frattini | C4 | C2×D127 |
| Fitting | C8×C127 | C2 |
| socle | C2×C127 | C2×C4 |
| prime radical | C2×D127 | C4 |
| cosocle | C4×C127 | C22 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1016 |
520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D127, #16861148, C2×C8×D127, … |
| maximal normal subgroup of | C16×D127, #16861148, C2×C8×D127, … |
| maximal quotient of | C8×Dic127, (C2×D127)⋊C8, Dic127⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2032, 21);