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ΓL(1,𝔽8)×D141 #20238367

order5922
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D141
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×D47)
unambiguous semidirect productC47⋊(D3×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D141)⋊C3

Splittings

Fitting, socle, derivedC3×C7×C47 ⋊ C2×C3
HallC3×ΓL(1,𝔽8)×C47 ⋊ C2
HallC7×C47 ⋊ C3×D3
HallC3×ΓL(1,𝔽8) ⋊ D47
SylowC47 ⋊ D3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D141

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C7×C47C2×C3
LCSG ▷ C3×C7×C47
UCSC1

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D141, (C3⋊AGL(1,𝔽7))⋊D47, D3×ΓL(1,𝔽8)×D47, …
maximal normal subgroup ofAGL(1,𝔽7)×D141, (C3⋊AGL(1,𝔽7))⋊D47, D3×ΓL(1,𝔽8)×D47, …
maximal quotient ofΓL(1,𝔽8)×Dic141, C2×ΓL(1,𝔽8)×D141, C5×ΓL(1,𝔽8)×D141, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5922, 20);