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C2×C3×C5×ΓL(1,𝔽8)×C47 #44444104

order29610
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C47 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×ΓL(1,𝔽8)×C47
unambiguous semidirect product(C2×C7)⋊(C32×C5×C47)
unambiguous semidirect product(C2×C3×C7)⋊(C3×C5×C47)
unambiguous semidirect product(C2×C5×C7)⋊(C32×C47)
unambiguous semidirect product(C2×C3×C5×C7)⋊(C3×C47)
unambiguous semidirect product(C2×C7×C47)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C7×C47)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C47)⋊C32
unambiguous semidirect product(C2×C3×C5×C7×C47)⋊C3

Splittings

Fitting, socleC2×C3×C5×C7×C47 ⋊ C3
derived, SylowC7 ⋊ C2×C32×C5×C47
HallC2×C5×C7×C47 ⋊ C32
HallC5×C7×C47 ⋊ C2×C32
HallC2×C7×C47 ⋊ C32×C5
HallC7×C47 ⋊ C2×C32×C5
HallC2×C5×C7 ⋊ C32×C47
HallC5×C7 ⋊ C2×C32×C47
HallC2×C7 ⋊ C32×C5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C47ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C32×C5×C47
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C47C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C47

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9870

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 41);