Finite Group DatabasebetaFinite Group Databasebeta| order | 17775 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C52⋊(C79⋊C3) |
| unambiguous semidirect product | (C3×C52)⋊(C79⋊C3) |
| unambiguous semidirect product | (C3×C79)⋊(C52⋊C3) |
| Fitting, socle | C3×C52×C79 ⋊ C3 |
| derived, Hall | C52×C79 ⋊ C32 |
| Sylow | C79 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C52⋊(C79⋊C3) |
| commutator, cosocle, hypocenter | C52×C79 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C79 | C3 |
| LCS | G ▷ C52×C79 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3555 |
1983 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D79⋊(C52⋊C3), C3×#26045007, C3×(C5⋊D5)⋊(C79⋊C3), … |
| maximal normal subgroup of | C3×D79⋊(C52⋊C3), C3×#26045007, C3×(C5⋊D5)⋊(C79⋊C3), … |
| maximal quotient of | C2×C3×C52⋊(C79⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17775, 11);