Finite Group DatabasebetaFinite Group Databasebeta| order | 19275 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C257 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×C257 |
| unambiguous semidirect product | C52⋊(C3×C257) |
| unambiguous semidirect product | (C52×C257)⋊C3 |
| Fitting, socle, Hall | C52×C257 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C257 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C257 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C3×C257 |
| Frattini | C1 | G |
| Fitting, socle | C52×C257 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C257 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3855 |
2827 conjugacy classes. The character table is too large to display.
| derived subgroup of | C257⋊#3874 |
| maximal subgroup of | C52⋊C3×D257, #3874×C257, C257⋊#3874, … |
| maximal normal subgroup of | C52⋊C3×D257, #3874×C257, C257⋊#3874, … |
| maximal quotient of | C2×C52⋊C3×C257 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19275, 3);