Finite Group Databasebeta

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C2×C3×#66262 #14479017

order1920
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C3×#66262
unambiguous semidirect productD5⋊(C3×#519)

Splittings

FittingC22×C3×C5×Q8 ⋊ C4
HallC3×C5 ⋊ C2×#519
SylowC5 ⋊ C2×C3×#519

Subgroups

subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC2×C5C24×C3×C4
FrattiniC2C24×C3×AGL(1,𝔽5)
FittingC22×C3×C5×Q8C4
socleC22×C3×C5C23×C4
prime radicalC23×C3×D5C23
cosocleC2×D5C25×C3
hypercenterC22×C3×Q8AGL(1,𝔽5)
hypocenterC5C2×C3×#519
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×Q8

2976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204715);