Finite Group Databasebeta

← Prev (#30655994) Next (#30655996) →

ΓL(1,𝔽8)×D391 #30655995

order16422
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D391
unambiguous semidirect productC17⋊(ΓL(1,𝔽8)×D23)
unambiguous semidirect productC23⋊(ΓL(1,𝔽8)×D17)
unambiguous semidirect product(C7×D391)⋊C3

Splittings

Fitting, socle, derived, HallC7×C17×C23 ⋊ C2×C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C2
HallC7×D391 ⋊ C3
HallΓL(1,𝔽8)×C23 ⋊ D17
HallC17×C23 ⋊ C2×ΓL(1,𝔽8)
HallC17×ΓL(1,𝔽8) ⋊ D23
HallC7×C23 ⋊ C3×D17
HallC7×C17 ⋊ C3×D23
SylowC23 ⋊ ΓL(1,𝔽8)×D17
SylowC17 ⋊ ΓL(1,𝔽8)×D23
SylowC7 ⋊ C3×D391

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C17×C23C2×C3
LCSG ▷ C7×C17×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽7)×D391, (C17⋊AGL(1,𝔽7))⋊D23, ΓL(1,𝔽8)×D17×D23, …
maximal normal subgroup ofAGL(1,𝔽7)×D391, (C17⋊AGL(1,𝔽7))⋊D23, ΓL(1,𝔽8)×D17×D23, …
maximal quotient ofΓL(1,𝔽8)×Dic391, C2×ΓL(1,𝔽8)×D391

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16422, 20);