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C2×C5×ΓL(1,𝔽8)×C43⋊C3 #41029147

order27090
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C43⋊C3
unambiguous semidirect product(C2×C7×C43⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×ΓL(1,𝔽8)×C43)⋊(C3×C5)
unambiguous semidirect product(C2×#11744748)⋊(C3×C5)
unambiguous semidirect product(C2×#11744749)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C43⋊C3)⋊C3
unambiguous semidirect product(C2×C5×ΓL(1,𝔽8)×C43)⋊C3
unambiguous semidirect product(C2×C5×#11744749)⋊C3
unambiguous semidirect product(C2×C5×#11744748)⋊C3

Splittings

Fitting, socle, HallC2×C5×C7×C43 ⋊ C32
derived, HallC7×C43 ⋊ C2×C32×C5
HallC5×C7×C43 ⋊ C2×C32
HallC2×C7×C43 ⋊ C32×C5
HallC2×C5×C43 ⋊ C3×ΓL(1,𝔽8)
HallC5×C43 ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C43 ⋊ C3×C5×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C3×C43⋊C3
SylowC43 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×C43⋊C3
HallC2×C7 ⋊ C3×C5×C43⋊C3
SylowC7 ⋊ C2×C3×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×C43⋊C3
commutator, cosocle, hypocenterC7×C43C2×C32×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C43C32
LCSG ▷ C7×C43
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3010

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27090, 88);