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C2×C13×C3⋊(C7⋊D7) #21439799

order7644
isoclinismisoclinic class of C3⋊(C7⋊D7)
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C13×C3⋊(C7⋊D7)
unambiguous semidirect product(C2×C3)⋊(C13×C7⋊D7)
unambiguous semidirect product(C2×C7)⋊(C13×D21)

Splittings

Fitting, socleC2×C3×C72×C13 ⋊ C2
derived, HallC3×C72 ⋊ C22×C13
HallC3×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×D3
SylowC72 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×C7⋊D7
SylowC3 ⋊ C2×C13×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(C7⋊D7)
commutator, hypocenterC3×C72C22×C13
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2
LCSG ▷ C3×C72
UCSC1 ◁ C2×C13

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×C7⋊D63, C2×C13×C3⋊(ΓL(1,𝔽8)⋊D7), C2×C3⋊#16838470, …
maximal normal subgroup ofC2×C13×C3⋊(ΓL(1,𝔽8)⋊D7), C2×C3⋊#16838470, C2×C3⋊#16838471, …
maximal quotient ofC2×C13×C7⋊D63, D3×C13×C3⋊(C7⋊D7), C2×C3×C13×C3⋊(C7⋊D7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 368);