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C5×ΓL(1,𝔽8)×D83 #31775238

order17430
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D83
unambiguous semidirect productC83⋊(C2×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D83)⋊(C3×C5)
unambiguous semidirect product(C5×C7×D83)⋊C3

Splittings

Fitting, socle, HallC5×C7×C83 ⋊ C2×C3
derived, HallC7×C83 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C83 ⋊ C2
HallC5×C7×D83 ⋊ C3
HallΓL(1,𝔽8)×C83 ⋊ C2×C5
HallC7×D83 ⋊ C3×C5
HallC5×C83 ⋊ C2×ΓL(1,𝔽8)
SylowC83 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D83
SylowC7 ⋊ C3×C5×D83

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D83
commutator, cosocle, hypocenterC7×C83C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C83C2×C3
LCSG ▷ C7×C83
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2905

Conjugacy classes & character table

1075 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D83, D83×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D83, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D83, D83×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)×D83, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic83, C2×C5×ΓL(1,𝔽8)×D83

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 18);