Finite Group Databasebeta

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C3×C17×C131⋊C5 #45689111

order33405
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×C131⋊C5
unambiguous semidirect productC131⋊(C3×C5×C17)
unambiguous semidirect product(C3×C131)⋊(C5×C17)
unambiguous semidirect product(C17×C131)⋊(C3×C5)
unambiguous semidirect product(C3×C17×C131)⋊C5

Splittings

Fitting, socle, HallC3×C17×C131 ⋊ C5
derived, SylowC131 ⋊ C3×C5×C17
HallC17×C131 ⋊ C3×C5
HallC3×C131 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17C131⋊C5
commutator, cosocle, hypocenterC131C3×C5×C17
FrattiniC1G
Fitting, socleC3×C17×C131C5
LCSG ▷ C131
UCSC1 ◁ C3×C17

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6681

Conjugacy classes & character table

1581 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33405, 2);