Finite Group DatabasebetaFinite Group Databasebeta| order | 17775 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×C79⋊C9 |
| unambiguous semidirect product | C79⋊(C52×C9) |
| unambiguous semidirect product | (C5×C79)⋊(C5×C9) |
| derived, Sylow | C79 ⋊ C52×C9 |
| Hall | C52×C79 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C79⋊C3 |
| commutator, hypocenter | C79 | C52×C9 |
| Frattini | C3 | C52×C79⋊C3 |
| Fitting, socle, prime radical | C3×C52×C79 | C3 |
| cosocle | C3×C79 | C3×C52 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C52 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17775 |
2175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D79⋊C9, C5×C5⋊(D79⋊C9), C5×D5×C79⋊C9, … |
| maximal normal subgroup of | C52×D79⋊C9, C5×C5⋊(D79⋊C9), C5×D5×C79⋊C9, … |
| maximal quotient of | C2×C52×C79⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17775, 6);