Finite Group Databasebeta

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C22×C3×#4007 #14412253

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C3×#4007
unambiguous semidirect productD5⋊(C2×C3×#102)

Splittings

FittingC22×C3×C5×D4 ⋊ C4
HallC3×C5 ⋊ C22×#102
SylowC5 ⋊ C22×C3×#102

Subgroups

subgroupG/H
centerC23×C3C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC23×C3×C5C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC4×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C22×C3×#102
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137951);