Finite Group DatabasebetaFinite Group Databasebeta| order | 2540 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C127 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C127 |
| unambiguous semidirect product | C5⋊(C22×C127) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C127) |
| Fitting, socle | C2×C5×C127 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C127 |
| Hall | C5×C127 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C127 | D5 |
| commutator, cosocle, hypocenter | C5 | C22×C127 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C127 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C127 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1270 |
1016 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D25×C127, D52×C127, C2×C5⋊D5×C127, … |
| maximal normal subgroup of | C2×C5×D5×C127, C2×D5×C127⋊C7, C2×C7×D5×C127, … |
| maximal quotient of | C2×D25×C127, D52×C127, C2×C5⋊D5×C127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2540, 10);