Finite Group DatabasebetaFinite Group Databasebeta| order | 19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C127 · Schur multiplier (H2) = C5 |
| direct product | C127×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5)⋊(C3×C127) |
| Fitting, socle, Hall | C52×C127 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C2×C3×C127 |
| Hall | C52⋊C3×C127 ⋊ C2 |
| Hall | C5⋊D5×C127 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C127 |
| Hall | C5⋊D5 ⋊ C3×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C3×C127 |
| Frattini | C1 | G |
| Fitting, socle | C52×C127 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C127 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1905 |
1270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C5⋊D5)⋊C3×D127, C127×#64480, C127⋊#64480, … |
| maximal normal subgroup of | (C5⋊D5)⋊C3×D127, C127×#64480, C127⋊#64480, … |
| maximal quotient of | C127×#1039⋊C3, C2×C127×(C5⋊D5)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19050, 21);