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C2×C5⋊(ΓL(1,𝔽8)⋊D13) #19129803

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(ΓL(1,𝔽8)⋊D13)
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)⋊D13)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D65

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC5×C7×C13 ⋊ C22×C3
HallC2×D455 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C22
HallC13×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×ΓL(1,𝔽8) ⋊ C2×D13
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×D65
SylowC13 ⋊ C2×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D65
SylowC5 ⋊ C2×ΓL(1,𝔽8)⋊D13

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(ΓL(1,𝔽8)⋊D13)
commutator, hypocenterC5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

334 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), D3×C5⋊(ΓL(1,𝔽8)⋊D13), C2×C3×C5⋊(ΓL(1,𝔽8)⋊D13), …
maximal normal subgroup ofC2×C5⋊(ΓL(1,𝔽8)⋊(D13⋊C3)), C2×C3×C5⋊(ΓL(1,𝔽8)⋊D13), C2×C5×C5⋊(ΓL(1,𝔽8)⋊D13), …
maximal quotient ofC2×C5⋊((C7⋊C9)⋊D13), D3×C5⋊(ΓL(1,𝔽8)⋊D13), C2×C3×C5⋊(ΓL(1,𝔽8)⋊D13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 145);