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C3×C47⋊((C19⋊C3)⋊C4) #44565281

order32148
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C47⋊((C19⋊C3)⋊C4)
unambiguous semidirect productC47⋊(C3×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C3×Dic47)
unambiguous semidirect productDic893⋊C32
unambiguous semidirect product(C3×Dic893)⋊C3

Splittings

derived, HallC19×C47 ⋊ C32×C4
HallC3×C47×C19⋊C3 ⋊ C4
HallDic893 ⋊ C32
HallC3×C19⋊C3 ⋊ Dic47
SylowC47 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C3C47⋊(D19⋊C3)
commutator, hypocenterC19×C47C32×C4
FrattiniC2C3×C47⋊(D19⋊C3)
Fitting, socleC2×C3×C19×C47C2×C3
prime radicalC2×C3×C47×C19⋊C3C2
cosocleC2×C19×C47C2×C32
LCSG ▷ C19×C47
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10716

Conjugacy classes & character table

1296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 41);