Finite Group Databasebeta

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C2×C49×C3⋊D39 #37524314

order22932
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C49×C3⋊D39
unambiguous semidirect product(C2×C3)⋊(C49×D39)
unambiguous semidirect product(C2×C13)⋊(C3⋊D3×C49)

Splittings

FittingC2×C32×C13×C49 ⋊ C2
derived, HallC32×C13 ⋊ C22×C49
HallC32×C13×C49 ⋊ C22
HallC13×C49 ⋊ C2×C3⋊D3
HallC32×C49 ⋊ C2×D13
SylowC13 ⋊ C2×C3⋊D3×C49
SylowC32 ⋊ C2×D13×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49C3⋊D39
commutator, hypocenterC32×C13C22×C49
FrattiniC7C2×C7×C3⋊D39
FittingC2×C32×C13×C49C2
socleC2×C32×C7×C13C2×C7
prime radicalC2×C7×C3⋊D39C7
cosocleC32×C7×C13C22×C7
LCSG ▷ C32×C13
UCSC1 ◁ C2×C49

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

5880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 259);