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C47×C3⋊(Dic13⋊C3) #36347204

order21996
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C47×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C47)
unambiguous semidirect product(C47×Dic39)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C47
HallC3×C13⋊C3×C47 ⋊ C4
HallC13×C47 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C47
SylowC13 ⋊ C3×Dic3×C47

Subgroups

subgroupG/H
center, hypercenterC2×C47C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C47
FrattiniC2C47×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C47C2×C3
prime radicalC2×C3×C13⋊C3×C47C2
cosocleC2×C3×C13C2×C3×C47
LCSG ▷ C3×C13
UCSC1 ◁ C2×C47

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7332

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 45);