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C2×C72×D13⋊C3 #21439689

order7644
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C72)
unambiguous semidirect product(C13⋊C3)⋊(C22×C72)
unambiguous semidirect product(C2×D13)⋊(C3×C72)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C72)

Splittings

Fitting, socleC2×C72×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C72
HallC2×C72×D13 ⋊ C3
HallC72×C13⋊C3 ⋊ C22
HallC72×C13 ⋊ C22×C3
HallC2×D13 ⋊ C3×C72
HallC13⋊C3 ⋊ C22×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72D13⋊C3
commutator, hypocenterC13C22×C3×C72
FrattiniC1G
Fitting, socleC2×C72×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C72

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×ΓL(1,𝔽8)×D13⋊C3, C2×D13⋊C3×#3861, C2×D13⋊C3×#3862, …
maximal normal subgroup ofC2×C7×ΓL(1,𝔽8)×D13⋊C3, C2×D13⋊C3×#3861, C2×D13⋊C3×#3862, …
maximal quotient ofC2×C72×D13⋊C9, D3×C72×D13⋊C3, C2×C3×C72×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 258);