Finite Group Databasebeta

← Prev (#44568426) Next (#44568428) →

C2×C3×C11×D245 #44568427

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D245
unambiguous semidirect product(C2×C5)⋊(C3×C11×D49)

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC5×C49 ⋊ C22×C3×C11
HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C22×C3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C22×C11
HallC11×C49 ⋊ C2×C3×D5
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C3×D49
SylowC49 ⋊ C2×C3×D5×C11
HallC3×C5 ⋊ C2×C11×D49
SylowC5 ⋊ C2×C3×C11×D49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D245
commutator, cosocle, hypocenterC5×C49C22×C3×C11
FrattiniC7C2×C3×C11×D35
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C5×C49
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

8184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 129);