Finite Group Databasebeta

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C47×#63120⋊C3 #49144013

order36660
automorphism?
homologyAbelianization (H1) = C3×C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×#63120⋊C3
unambiguous semidirect product#63120⋊(C3×C47)
unambiguous semidirect product(C47×#63120)⋊C3

Splittings

Fitting, socle, HallC5×C13×C47 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C47
HallC47×#63120 ⋊ C3
HallC5×C13⋊C3×C47 ⋊ C4
HallC13⋊C3×C47 ⋊ AGL(1,𝔽5)
HallC13×C47 ⋊ C3×AGL(1,𝔽5)
Hall#63120 ⋊ C3×C47
HallC5×C47 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C4×C47
HallC13⋊C3 ⋊ AGL(1,𝔽5)×C47
SylowC13 ⋊ C3×AGL(1,𝔽5)×C47
SylowC5 ⋊ C47×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC47#63120⋊C3
commutator, hypocenterC5×C13C3×C4×C47
FrattiniC1G
Fitting, socleC5×C13×C47C3×C4
prime radicalD5×C13⋊C3×C47C2
cosocleD5×C13C2×C3×C47
LCSG ▷ C5×C13
UCSC1 ◁ C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3055

Conjugacy classes & character table

1081 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 33);