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C2×C3×C22⋊C4×AGL(1,𝔽5) #14319387

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C3×C22⋊C4×AGL(1,𝔽5)

Splittings

FittingC2×C3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ C2×C4×C22⋊C4
SylowC5 ⋊ C2×C3×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC2×C5C22×C3×C42
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC22×D5C24×C3
hypercenterC2×C3×C22⋊C4AGL(1,𝔽5)
hypocenterC5C2×C3×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

2720 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.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×#120, C22⋊C4×AGL(1,𝔽5)×AGL(1,𝔽7)
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×#120
maximal quotient ofC22⋊C4×AGL(1,𝔽5)×AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45085);