Finite Group Databasebeta

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C2×C3×C11⋊C5×D49 #44568363

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11⋊C5×D49
unambiguous semidirect product(C2×C3×C11×D49)⋊C5

Splittings

FittingC2×C3×C11×C49 ⋊ C2×C5
derived, HallC11×C49 ⋊ C22×C3×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallC2×C3×C11×D49 ⋊ C5
HallC49×C11⋊C5 ⋊ C22×C3
HallC2×C11×D49 ⋊ C3×C5
HallC3×C11×C49 ⋊ C22×C5
HallC3×C49 ⋊ C22×C11⋊C5
SylowC49 ⋊ C22×C3×C11⋊C5
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C2×C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×D49
commutator, cosocle, hypocenterC11×C49C22×C3×C5
FrattiniC7C2×C3×D7×C11⋊C5
FittingC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 65);