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C2×C3×C16×AGL(1,𝔽5) #14312512

order1920
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C3×C16×AGL(1,𝔽5)

Splittings

FittingC2×C3×C5×C16 ⋊ C4
derived, SylowC5 ⋊ C2×C3×C4×C16
HallC3×C5 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC2×C3×C16AGL(1,𝔽5)
commutator, hypocenterC5C2×C3×C4×C16
FrattiniC8C22×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C16C4
socleC22×C3×C5C4×C8
prime radicalC22×C3×D5C2×C8
cosocleC8×D5C23×C3
LCSG ▷ C5
UCSC1 ◁ C2×C3×C16

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38210);