Finite Group DatabasebetaFinite Group Databasebeta| order | 9220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic461 |
| derived, Sylow | C461 ⋊ C4×C5 |
| Hall | C5×C461 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D461 |
| commutator, hypocenter | C461 | C4×C5 |
| Frattini | C2 | C5×D461 |
| Fitting, socle | C2×C5×C461 | C2 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic461, C5×Dic1383 |
| maximal normal subgroup of | C3×C5×Dic461 |
| maximal quotient of | C3×C5×Dic461, C5×Dic1383 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9220, 5);