Finite Group Databasebeta

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C3×#10598766 #14276857

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10598766

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ #1282
SylowC5 ⋊ C3×#1282

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C3×C4×C8
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5C2×C4
cosocleC22×C4×D5C22×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1282
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8

456 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, 2555);