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C3×C5×ΓL(1,𝔽8)×C83 #39908481

order26145
automorphism?
homologyAbelianization (H1) = C32×C5×C83 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)×C83
unambiguous semidirect productC7⋊(C32×C5×C83)
unambiguous semidirect product(C3×C7)⋊(C3×C5×C83)
unambiguous semidirect product(C5×C7)⋊(C32×C83)
unambiguous semidirect product(C3×C5×C7)⋊(C3×C83)
unambiguous semidirect product(C7×C83)⋊(C32×C5)
unambiguous semidirect product(C3×C7×C83)⋊(C3×C5)
unambiguous semidirect product(C5×C7×C83)⋊C32
unambiguous semidirect product(C3×C5×C7×C83)⋊C3

Splittings

Fitting, socleC3×C5×C7×C83 ⋊ C3
derived, SylowC7 ⋊ C32×C5×C83
HallC5×C7×C83 ⋊ C32
HallC7×C83 ⋊ C32×C5
HallC5×C7 ⋊ C32×C83

Subgroups

subgroupG/H
center, hypercenterC3×C5×C83ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C5×C83
FrattiniC1G
Fitting, socleC3×C5×C7×C83C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C83

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

6225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26145, 4);