Finite Group Databasebeta

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C3×C17×C121⋊C5 #44524802

order30855
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×C121⋊C5
unambiguous semidirect productC121⋊(C3×C5×C17)
unambiguous semidirect product(C3×C121)⋊(C5×C17)
unambiguous semidirect product(C17×C121)⋊(C3×C5)
unambiguous semidirect product(C3×C17×C121)⋊C5

Splittings

Fitting, HallC3×C17×C121 ⋊ C5
derived, SylowC121 ⋊ C3×C5×C17
HallC17×C121 ⋊ C3×C5
HallC3×C121 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17C121⋊C5
commutator, cosocle, hypocenterC121C3×C5×C17
FrattiniC11C3×C17×C11⋊C5
FittingC3×C17×C121C5
socleC3×C11×C17C11⋊C5
LCSG ▷ C121
UCSC1 ◁ C3×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6171

Conjugacy classes & character table

1479 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30855, 2);