Finite Group Databasebeta

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C3×#10604721 #14294563

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#10604721

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ #1735
SylowC5 ⋊ C3×#1735

Subgroups

subgroupG/H
centerC2×C3×C4C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C4×D5C23×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C3×#1735
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8

848 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, 20261);