Finite Group Databasebeta

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C41×C3⋊(Dic13⋊C3) #34062905

order19188
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C41×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C41)
unambiguous semidirect product(C41×Dic39)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C41
HallC3×C13⋊C3×C41 ⋊ C4
HallC13×C41 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C41
SylowC13 ⋊ C3×Dic3×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C41
FrattiniC2C41×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C41C2×C3
prime radicalC2×C3×C13⋊C3×C41C2
cosocleC2×C3×C13C2×C3×C41
LCSG ▷ C3×C13
UCSC1 ◁ C2×C41

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

1230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 57);