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C5×C22⋊#63271 #19129879

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

Aliases

direct productC5×C22⋊#63271
unambiguous semidirect productC22⋊(C5×#63271)
unambiguous semidirect product(C22×C5)⋊#63271

Splittings

Fitting, socle, HallC22×C5×C7×C13 ⋊ C3
derived, HallC22×C7×C13 ⋊ C3×C5
HallC5×C7×C13 ⋊ A4
HallC22×C5×C13 ⋊ ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C13⋊C3
HallC7×C13 ⋊ C5×A4
HallC5×C13 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C13 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22⋊(C13⋊C3)
HallC22×C7 ⋊ C5×C13⋊C3
HallC22×C5 ⋊ #63271
SylowC13 ⋊ C5×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C5×C22⋊(C13⋊C3)
SylowC22 ⋊ C5×#63271

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#63271
commutator, hypocenterC22×C7×C13C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C13C3
LCSG ▷ C22×C7×C13
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

620 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×C22⋊ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C5×A4×#63271, …
maximal normal subgroup ofC5×C13⋊C3×C22⋊ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C5×A4×#63271, …
maximal quotient ofC5×C22⋊#11717942, C3×C5×C22⋊#63271, C25×C22⋊#63271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 221);