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C3×C13⋊C3×Dic47 #36347203

order21996
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×Dic47
unambiguous semidirect productC47⋊(C3×C4×C13⋊C3)
unambiguous semidirect product(C13×Dic47)⋊C32
unambiguous semidirect product(C3×C13×Dic47)⋊C3

Splittings

derived, HallC13×C47 ⋊ C32×C4
HallC3×C13⋊C3×C47 ⋊ C4
HallC13×Dic47 ⋊ C32
SylowC47 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C32×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊C3×D47
commutator, hypocenterC13×C47C32×C4
FrattiniC2C3×C13⋊C3×D47
Fitting, socleC2×C3×C13×C47C2×C3
prime radicalC2×C3×C13⋊C3×C47C2
cosocleC2×C13×C47C2×C32
LCSG ▷ C13×C47
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7332

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 44);