Finite Group Databasebeta

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C103×D165 #46800929

order33990
automorphism?
homologyAbelianization (H1) = C2×C103 · Schur multiplier (H2) = C1

Aliases

direct productC103×D165
unambiguous semidirect productC3⋊(C103×D55)
unambiguous semidirect productC5⋊(D33×C103)
unambiguous semidirect productC11⋊(D15×C103)

Splittings

Fitting, socle, HallC3×C5×C11×C103 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C103
HallC5×C11×C103 ⋊ D3
HallC3×C11×C103 ⋊ D5
HallC3×C5×C103 ⋊ D11
HallC11×C103 ⋊ D15
HallC5×C103 ⋊ D33
HallC3×C103 ⋊ D55
HallC5×C11 ⋊ D3×C103
HallC3×C11 ⋊ D5×C103
HallC3×C5 ⋊ D11×C103
SylowC11 ⋊ D15×C103
SylowC5 ⋊ D33×C103
SylowC3 ⋊ C103×D55

Subgroups

subgroupG/H
center, hypercenterC103D165
commutator, cosocle, hypocenterC3×C5×C11C2×C103
FrattiniC1G
Fitting, socleC3×C5×C11×C103C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C103

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16995

Conjugacy classes & character table

8652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 18);