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C3×AGL(1,𝔽5)×#101 #14295472

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×AGL(1,𝔽5)×#101

Splittings

FittingC3×C5×#101 ⋊ C4
HallC3×C5 ⋊ C4×#101
SylowC5 ⋊ C3×C4×#101

Subgroups

subgroupG/H
centerC2×C3C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C5×#101C4
socleC2×C3×C5C4×C22⋊C4
prime radicalC22×C3×D5C22×C4
cosocleC2×C4×D5C23×C3
hypercenterC3×#101AGL(1,𝔽5)
hypocenterC5C3×C4×#101
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#101

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21170);