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C72×C22⋊(C13⋊C3) #21439787

order7644
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC72×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C72×C13⋊C3)
unambiguous semidirect productC13⋊(C72×A4)

Splittings

Fitting, socle, HallC22×C72×C13 ⋊ C3
derived, HallC22×C13 ⋊ C3×C72
HallC72×C13 ⋊ A4
HallC22×C72 ⋊ C13⋊C3
SylowC13 ⋊ C72×A4
SylowC22 ⋊ C72×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC72C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C3×C72
FrattiniC1G
Fitting, socleC22×C72×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C72

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC72×A4×C13⋊C3, C7×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C7×#63270⋊A4, …
maximal normal subgroup ofC72×A4×C13⋊C3, C7×ΓL(1,𝔽8)×C22⋊(C13⋊C3), C7×#63270⋊A4, …
maximal quotient ofC72×C22⋊(C13⋊C9), C3×C72×C22⋊(C13⋊C3), C5×C72×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 356);