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C3×AGL(1,𝔽5)×C169 #23778367

order10140
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C169 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C169

Splittings

Fitting, HallC3×C5×C169 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C169
HallC5×C169 ⋊ C3×C4
HallC3×C5 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC3×C169AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C169
FrattiniC13C3×C13×AGL(1,𝔽5)
FittingC3×C5×C169C4
socleC3×C5×C13C4×C13
prime radicalC3×D5×C13C2×C13
cosocleD5×C13C2×C3×C13
LCSG ▷ C5
UCSC1 ◁ C3×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C169⋊C9, C9×AGL(1,𝔽5)×C169, C3×AGL(1,𝔽5)×C169⋊C3, …
maximal normal subgroup ofAGL(1,𝔽5)×C169⋊C9, C9×AGL(1,𝔽5)×C169, C3×AGL(1,𝔽5)×C169⋊C3, …
maximal quotient ofC9×AGL(1,𝔽5)×C169, C32×AGL(1,𝔽5)×C169, C3×ΓL(1,𝔽16)×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 25);