Finite Group Databasebeta

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C3×AGL(1,𝔽5)×#117 #14319500

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC3×AGL(1,𝔽5)×#117

Splittings

FittingC3×C5×#117 ⋊ C4
HallC3×C5 ⋊ C4×#117
SylowC5 ⋊ C3×C4×#117

Subgroups

subgroupG/H
centerC2×C3×C4C22×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C42
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC3×C5×#117C4
socleC22×C3×C5C23×C4
prime radicalC23×C3×D5C23
cosocleC22×D5C24×C3
hypercenterC3×#117AGL(1,𝔽5)
hypocenterC5C3×C4×#117
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×#117

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45198);