Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic403 |
| derived, Hall | C13×C31 ⋊ C4×C5 |
| Hall | C5×C13×C31 ⋊ C4 |
| Hall | C5×C31 ⋊ Dic13 |
| Hall | C5×C13 ⋊ Dic31 |
| Sylow | C31 ⋊ C5×Dic13 |
| Sylow | C13 ⋊ C5×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D403 |
| commutator, hypocenter | C13×C31 | C4×C5 |
| Frattini | C2 | C5×D403 |
| Fitting, socle | C2×C5×C13×C31 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
2030 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic403, C5×Dic1209, C5×(C31⋊C3)⋊Dic13, … |
| maximal normal subgroup of | C3×C5×Dic403, C5×(C31⋊C3)⋊Dic13, C5×#18012818, … |
| maximal quotient of | C3×C5×Dic403, C5×Dic1209 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 5);