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Dic5×#914 #14416695

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productDic5×#914

Splittings

HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C4×#914
SylowC3 ⋊ Dic5×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#914C2
cosocleC2×C3×C4×C5C24
hypercenterC2×SD16D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142393);