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C3×ΓL(1,𝔽8)×C169 #24922387

order10647
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C32×C169 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C169
unambiguous semidirect productC7⋊(C32×C169)
unambiguous semidirect product(C3×C7)⋊(C3×C169)

Splittings

FittingC3×C7×C169 ⋊ C3
derived, SylowC7 ⋊ C32×C169
HallC7×C169 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C169ΓL(1,𝔽8)
commutator, hypocenterC7C32×C169
FrattiniC13C3×C13×ΓL(1,𝔽8)
FittingC3×C7×C169C3
socleC3×C7×C13C3×C13
prime radicalC3×C13×ΓL(1,𝔽8)C13
cosocleC7×C13C32×C13
LCSG ▷ C7
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 ofC3×ΓL(1,𝔽8)×D169, C3×AGL(1,𝔽7)×C169, C3×ΓL(1,𝔽8)⋊D169, …
maximal normal subgroup ofC3×ΓL(1,𝔽8)×D169, C3×AGL(1,𝔽7)×C169, C3×ΓL(1,𝔽8)⋊D169, …
maximal quotient ofC2×C3×ΓL(1,𝔽8)×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 9);