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ΓL(1,𝔽8)×C23×D17 #30655994

order16422
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C23×D17
unambiguous semidirect productC17⋊(C2×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C7×D17)⋊(C3×C23)
unambiguous semidirect product(C7×C23×D17)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC23ΓL(1,𝔽8)×D17
commutator, cosocle, hypocenterC7×C17C2×C3×C23
FrattiniC1G
Fitting, socleC7×C17×C23C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2737

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×ΓL(1,𝔽8)⋊#595, ΓL(1,𝔽8)⋊(C23⋊#595), C23×D17×AGL(1,𝔽7), …
maximal normal subgroup ofC23×ΓL(1,𝔽8)⋊#595, ΓL(1,𝔽8)⋊(C23⋊#595), C23×D17×AGL(1,𝔽7), …
maximal quotient ofΓL(1,𝔽8)×C23×Dic17, C2×ΓL(1,𝔽8)×C23×D17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16422, 19);