Finite Group DatabasebetaFinite Group Databasebeta| order | 6620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic331 |
| derived, Sylow | C331 ⋊ C4×C5 |
| Hall | C5×C331 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D331 |
| commutator, hypocenter | C331 | C4×C5 |
| Frattini | C2 | C5×D331 |
| Fitting, socle | C2×C5×C331 | C2 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
1670 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic331, C5×Dic993, C5×(C331⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C5×Dic331, C5×(C331⋊C3)⋊C4, Dic331⋊C25, … |
| maximal quotient of | C3×C5×Dic331, C5×Dic993, C25×Dic331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6620, 5);