Finite Group DatabasebetaFinite Group Databasebeta| order | 8655 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C577⋊C3 |
| unambiguous semidirect product | C577⋊(C3×C5) |
| unambiguous semidirect product | (C5×C577)⋊C3 |
| Fitting, socle, Hall | C5×C577 ⋊ C3 |
| derived, Sylow | C577 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C577⋊C3 |
| commutator, hypocenter | C577 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C577 | C3 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
975 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×C577⋊C3, C5×D577⋊C3, D5×C577⋊C3, … |
| maximal normal subgroup of | C2×C5×C577⋊C3, C5×D577⋊C3, D5×C577⋊C3, … |
| maximal quotient of | C2×C5×C577⋊C3, C5×#19104460, C3×C5×C577⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8655, 1);