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C5×ΓL(1,𝔽8)⋊D43 #22583306

order9030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D43
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D43)

Splittings

Fitting, socle, HallC5×C7×C43 ⋊ C2×C3
derived, HallC7×C43 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C43 ⋊ C2
HallC5×D301 ⋊ C3
HallΓL(1,𝔽8)×C43 ⋊ C2×C5
HallD301 ⋊ C3×C5
HallC5×C43 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D43
SylowC43 ⋊ C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×D43
HallΓL(1,𝔽8) ⋊ C5×D43
SylowC7 ⋊ C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D43
commutator, hypocenterC7×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D43, D5×ΓL(1,𝔽8)⋊D43, (C5⋊AGL(1,𝔽7))⋊D43, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D43, D5×ΓL(1,𝔽8)⋊D43, (C5⋊AGL(1,𝔽7))⋊D43, …
maximal quotient ofC5×ΓL(1,𝔽8)⋊Dic43, C2×C5×ΓL(1,𝔽8)⋊D43, C5×(C7⋊C9)⋊D43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 39);