Finite Group Databasebeta

← Prev (#44528324) Next (#44528326) →

C2×C53×D49⋊C3 #44528325

order31164
automorphism?
homologyAbelianization (H1) = C22×C3×C53 · Schur multiplier (H2) = C2

Aliases

direct productC2×C53×D49⋊C3
unambiguous semidirect productD49⋊(C2×C3×C53)
unambiguous semidirect product(C49⋊C3)⋊(C22×C53)
unambiguous semidirect product(C2×D49)⋊(C3×C53)
unambiguous semidirect product(C2×C49⋊C3)⋊(C2×C53)
unambiguous semidirect product(C2×C53×D49)⋊C3

Splittings

FittingC2×C49×C53 ⋊ C2×C3
derived, SylowC49 ⋊ C22×C3×C53
HallC2×C53×D49 ⋊ C3
HallC53×C49⋊C3 ⋊ C22
HallC49×C53 ⋊ C22×C3
HallC2×D49 ⋊ C3×C53
HallC49⋊C3 ⋊ C22×C53

Subgroups

subgroupG/H
center, hypercenterC2×C53D49⋊C3
commutator, cosocle, hypocenterC49C22×C3×C53
FrattiniC7C2×AGL(1,𝔽7)×C53
FittingC2×C49×C53C2×C3
socleC2×C7×C53AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C2×C53

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5194

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 17);