Finite Group Databasebeta

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C2×C13×D49⋊C9 #37524099

order22932
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D49⋊C9
unambiguous semidirect productD49⋊(C2×C9×C13)
unambiguous semidirect product(C2×D49)⋊(C9×C13)
unambiguous semidirect product(C49⋊C9)⋊(C22×C13)
unambiguous semidirect product(C2×C49⋊C9)⋊(C2×C13)

Splittings

derived, SylowC49 ⋊ C22×C9×C13
HallC13×C49⋊C9 ⋊ C22
HallC2×C13×D49 ⋊ C9
HallC13×C49 ⋊ C22×C9
HallC49⋊C9 ⋊ C22×C13
HallC2×D49 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D49⋊C3
commutator, hypocenterC49C22×C9×C13
FrattiniC3×C7C2×C13×AGL(1,𝔽7)
FittingC2×C3×C13×C49C2×C3
socleC2×C3×C7×C13AGL(1,𝔽7)
prime radicalC2×C3×C13×D49C3
cosocleC3×C49C22×C3×C13
LCSG ▷ C49
UCSC1 ◁ C2×C3×C13

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

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(22932, 44);