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C59×D165 #34085695

order19470
automorphism?
homologyAbelianization (H1) = C2×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×D165
unambiguous semidirect productC3⋊(C59×D55)
unambiguous semidirect productC5⋊(C59×D33)
unambiguous semidirect productC11⋊(D15×C59)

Splittings

Fitting, socle, HallC3×C5×C11×C59 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C59
HallC5×C11×C59 ⋊ D3
HallC3×C11×C59 ⋊ D5
HallC3×C5×C59 ⋊ D11
HallC11×C59 ⋊ D15
HallC5×C59 ⋊ D33
HallC3×C59 ⋊ D55
HallC5×C11 ⋊ D3×C59
HallC3×C11 ⋊ D5×C59
HallC3×C5 ⋊ D11×C59
SylowC11 ⋊ D15×C59
SylowC5 ⋊ C59×D33
SylowC3 ⋊ C59×D55

Subgroups

subgroupG/H
center, hypercenterC59D165
commutator, cosocle, hypocenterC3×C5×C11C2×C59
FrattiniC1G
Fitting, socleC3×C5×C11×C59C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9735

Conjugacy classes & character table

4956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 16);