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C2×C3×#65779 #14320290

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C3×#65779
unambiguous semidirect productD5⋊(C3×#386)

Splittings

FittingC22×C3×C5×D4 ⋊ C4
HallC3×C5 ⋊ C2×#386
SylowC5 ⋊ C2×C3×#386

Subgroups

subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC23×C3×C5C22×C4
prime radicalC22×C3×D4×D5C2
cosocleC22×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C2×C3×#386
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×D4

3152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×#120, AGL(1,𝔽7)×#65779
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×#120
maximal quotient ofAGL(1,𝔽7)×#65779

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45988);