Finite Group Databasebeta

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#170×#208 #14280412

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#170×#208

Splittings

HallC3×C5 ⋊ C8×M16
SylowC5 ⋊ C8×#208
SylowC3 ⋊ M16×#170

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C42
prime radicalC23×C3×C5C42
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C8×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6110);