Finite Group Databasebeta

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C2×C11⋊C5×C3⋊(C7⋊D7) #44568759

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C11⋊C5×C3⋊(C7⋊D7)
unambiguous semidirect product(C2×C3)⋊(C11⋊C5×C7⋊D7)
unambiguous semidirect product(C2×C7)⋊(D21×C11⋊C5)
unambiguous semidirect product(C2×C11×C3⋊(C7⋊D7))⋊C5

Splittings

Fitting, socleC2×C3×C72×C11 ⋊ C2×C5
derived, HallC3×C72×C11 ⋊ C22×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC2×C11×C3⋊(C7⋊D7) ⋊ C5
HallC72×C11⋊C5 ⋊ C2×D3
HallC72×C11 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C2×C5×C7⋊D7
SylowC11 ⋊ C2×C5×C3⋊(C7⋊D7)
SylowC3 ⋊ C2×C11⋊C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C3⋊(C7⋊D7)
commutator, cosocle, hypocenterC3×C72×C11C22×C5
FrattiniC1G
Fitting, socleC2×C3×C72×C11C2×C5
LCSG ▷ C3×C72×C11
UCSC1 ◁ C2

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 461);