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C2×C7×D455 #27164972

order12740
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D455
unambiguous semidirect product(C2×C5)⋊(C7×D91)
unambiguous semidirect product(C2×C7)⋊(C7×D65)
unambiguous semidirect product(C2×C13)⋊(C7×D35)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2
derivedC5×C7×C13 ⋊ C22×C7
HallC5×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×D5
HallC5×C72 ⋊ C2×D13
HallC5×C13 ⋊ C2×C7×D7
SylowC72 ⋊ C2×D65
SylowC13 ⋊ C2×C7×D35
SylowC5 ⋊ C2×C7×D91

Subgroups

subgroupG/H
center, hypercenterC2×C7D455
commutator, cosocle, hypocenterC5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3206 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C13⋊#64418), C2×C7×C5⋊#10587722, C2×C7×C5⋊#10587723, …
maximal normal subgroup ofC2×C7×C5⋊#10587722, C2×C7×C5⋊#10587723, C2×C7×C5⋊(ΓL(1,𝔽8)⋊D13), …
maximal quotient ofD3×C7×D455, C2×C3×C7×D455, C2×C7×D1365

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12740, 102);