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C7×C22⋊#63270 #21439781

order7644
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×C22⋊#63270
unambiguous semidirect productC22⋊(C7×#63270)

Splittings

Fitting, socle, HallC22×C72×C13 ⋊ C3
derivedC22×C7×C13 ⋊ C3×C7
HallC72×C13 ⋊ A4
HallC22×C72 ⋊ C13⋊C3
HallC22×C13 ⋊ C7×ΓL(1,𝔽8)
SylowC72 ⋊ C22⋊(C13⋊C3)
SylowC13 ⋊ C7×C22⋊ΓL(1,𝔽8)
SylowC22 ⋊ C7×#63270

Subgroups

subgroupG/H
center, hypercenterC7C22⋊#63270
commutator, hypocenterC22×C7×C13C3×C7
FrattiniC1G
Fitting, socleC22×C72×C13C3
LCSG ▷ C22×C7×C13
UCSC1 ◁ C7

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C13⋊C3×C22⋊ΓL(1,𝔽8), C7×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C7×A4×#63270, …
maximal normal subgroup ofC7×C13⋊C3×C22⋊ΓL(1,𝔽8), C7×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C7×A4×#63270, …
maximal quotient ofC7×C22⋊#11717941, C3×C7×C22⋊#63270, C5×C7×C22⋊#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 350);