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C3×(C13⋊C3)⋊(C7⋊D7) #26039628

order11466
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7

Aliases

direct productC3×(C13⋊C3)⋊(C7⋊D7)
unambiguous semidirect product(C13⋊C3)⋊(C3×C7⋊D7)

Splittings

Fitting, socleC3×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C32
HallC3×C72×C13⋊C3 ⋊ C2
HallC7⋊D91 ⋊ C32
HallC3×C13⋊C3 ⋊ C7⋊D7
SylowC72 ⋊ C3×D13⋊C3
SylowC13 ⋊ C32×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊(C7⋊D7)
commutator, cosocle, hypocenterC72×C13C2×C32
FrattiniC1G
Fitting, socleC3×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C3

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

528 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#21439686, C3×D7×(C13⋊C3)⋊D7, C3×D13⋊C3×C7⋊D7, …
maximal normal subgroup ofC3×#21439686, C3×D7×(C13⋊C3)⋊D7, C3×D13⋊C3×C7⋊D7, …
maximal quotient ofC3×#21439560, C2×C3×(C13⋊C3)⋊(C7⋊D7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 271);