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C2×D5×C13×ΓL(1,𝔽8) #19129804

order5460
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C13×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C22×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C5)⋊(C2×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D5)⋊(C3×C13)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC5×C7 ⋊ C22×C3×C13
HallC2×C7×D5×C13 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×C7×D5 ⋊ C3×C13
HallC5×ΓL(1,𝔽8) ⋊ C22×C13
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C22×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×D5×C13
SylowC5 ⋊ C22×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C13D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C22×C3×C13
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, D3×D5×C13×ΓL(1,𝔽8), C2×C3×D5×C13×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, C2×C3×D5×C13×ΓL(1,𝔽8), C2×C5×D5×C13×ΓL(1,𝔽8), …
maximal quotient ofC2×D5×C13×C7⋊C9, D3×D5×C13×ΓL(1,𝔽8), C2×C3×D5×C13×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 146);