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C5×C13×ΓL(1,𝔽8)⋊C4 #19129684

order5460
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C5×C13)
unambiguous semidirect productDic7⋊(C3×C5×C13)
unambiguous semidirect product(C5×Dic7)⋊(C3×C13)

Splittings

derived, SylowC7 ⋊ C3×C4×C5×C13
HallC5×C13×Dic7 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC13×Dic7 ⋊ C3×C5
HallC13×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×Dic7 ⋊ C3×C13
HallC5×ΓL(1,𝔽8) ⋊ C4×C13
HallC7×C13 ⋊ C3×C4×C5
HallC5×C7 ⋊ C3×C4×C13
HallDic7 ⋊ C3×C5×C13
HallΓL(1,𝔽8) ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C5×C13
FrattiniC2C5×C13×AGL(1,𝔽7)
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

910 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×C13×ΓL(1,𝔽8)⋊C4, C5×C13×C3⋊(ΓL(1,𝔽8)⋊C4), …
maximal normal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×C13×ΓL(1,𝔽8)⋊C4, C13×C25×ΓL(1,𝔽8)⋊C4, …
maximal quotient ofC5×C13×Dic7⋊C9, C3×C5×C13×ΓL(1,𝔽8)⋊C4, C5×C13×C3⋊(ΓL(1,𝔽8)⋊C4), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 26);