Finite Group Databasebeta

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C3×C49×Dic39 #37524173

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×Dic39
unambiguous semidirect productC3⋊(C3×C49×Dic13)

Splittings

derivedC3×C13 ⋊ C3×C4×C49
HallC32×C13×C49 ⋊ C4
HallC13×C49 ⋊ C3×Dic3
HallC32×C49 ⋊ Dic13
HallC32×C13 ⋊ C4×C49
SylowC13 ⋊ C3×Dic3×C49
SylowC32 ⋊ C49×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C49D39
commutator, hypocenterC3×C13C3×C4×C49
FrattiniC2×C7C3×C7×D39
FittingC2×C32×C13×C49C2
socle, prime radicalC2×C32×C7×C13C2×C7
cosocleC2×C3×C7×C13C2×C3×C7
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3×C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

6174 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 118);