Finite Group Databasebeta

← Prev (#14296123) Next (#14296125) →

C4×#91177 #14296124

order1920
isoclinismisoclinic class of (C2×D3)⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#91177

Splittings

HallC3×C5 ⋊ C4×C4⋊C8
SylowC5 ⋊ C4×Dic3⋊C8
SylowC3 ⋊ C4×#4004

Subgroups

subgroupG/H
center, hypercenterC22×C4D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×Dic5C23
hypocenterC3×C5C4×C4⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4

632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21822);