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C2×C5×ΓL(1,𝔽8)⋊D13 #19129790

order5460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C5
HallC2×C5×D91 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×D91 ⋊ C3×C5
HallC13×ΓL(1,𝔽8) ⋊ C22×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×D13
HallC5×C13 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×C5×D13
SylowC13 ⋊ C2×C5×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C5×D13

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

370 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)⋊(D13⋊C3), C5×D3×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×C25×ΓL(1,𝔽8)⋊D13, …
maximal quotient ofC2×C5×(C7⋊C9)⋊D13, C5×D3×ΓL(1,𝔽8)⋊D13, C2×C3×C5×ΓL(1,𝔽8)⋊D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 132);