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C13×C22⋊#3862 #21439780

order7644
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C2×C7

Aliases

direct productC13×C22⋊#3862
unambiguous semidirect productC22⋊(C13×#3862)

Splittings

Fitting, socle, HallC22×C72×C13 ⋊ C3
derived, HallC22×C72 ⋊ C3×C13
HallC72×C13 ⋊ A4
HallC22×C13 ⋊ #3862
SylowC72 ⋊ A4×C13
SylowC22 ⋊ C13×#3862

Subgroups

subgroupG/H
center, hypercenterC13C22⋊#3862
commutator, hypocenterC22×C72C3×C13
FrattiniC1G
Fitting, socleC22×C72×C13C3
LCSG ▷ C22×C72
UCSC1 ◁ C13

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8), #37525399, #37525400, …
maximal normal subgroup ofC13×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8), #37525399, #37525400, …
maximal quotient ofC13×C22⋊#89205, C3×C13×C22⋊#3862, C5×C13×C22⋊#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 349);