Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#2202⋊C3 |
| unambiguous semidirect product | #2202⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2202)⋊C3 |
| Fitting, Hall | C5×#2202 ⋊ C3 |
| derived | H(3,𝔽4) ⋊ C2×C3×C5 |
| Sylow | #2202 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | B(4,𝔽2)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽4) | C2×C3×C5 |
| Frattini | C2×Q8 | C2×C5×A4 |
| Fitting | C5×#2202 | C3 |
| hypercenter | C22×C5 | #120⋊C3 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C2×C5 ◁ C22×C5 | |
156 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236398);