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C3×C167⋊AGL(1,𝔽5) #23756609

order10020
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C167⋊AGL(1,𝔽5)
unambiguous semidirect productC167⋊(C3×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C167 ⋊ C4
derived, HallC5×C167 ⋊ C3×C4
HallC3×C167 ⋊ AGL(1,𝔽5)
SylowC167 ⋊ C3×AGL(1,𝔽5)
HallC3×C5 ⋊ Dic167
SylowC5 ⋊ C3×Dic167

Subgroups

subgroupG/H
center, hypercenterC3C167⋊AGL(1,𝔽5)
commutator, hypocenterC5×C167C3×C4
FrattiniC1G
Fitting, socleC3×C5×C167C4
prime radicalC3×D5×C167C2
cosocleD5×C167C2×C3
LCSG ▷ C5×C167
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1011 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C167⋊AGL(1,𝔽5), C32×C167⋊AGL(1,𝔽5), C3×C3⋊(C167⋊AGL(1,𝔽5))
maximal normal subgroup ofC9×C167⋊AGL(1,𝔽5), C32×C167⋊AGL(1,𝔽5)
maximal quotient ofC9×C167⋊AGL(1,𝔽5), C32×C167⋊AGL(1,𝔽5), C3×C3⋊(C167⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10020, 11);