Finite Group Databasebeta

← Prev (#45686788) Next (#45686790) →

C101×D165 #45686789

order33330
automorphism?
homologyAbelianization (H1) = C2×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×D165
unambiguous semidirect productC3⋊(C101×D55)
unambiguous semidirect productC5⋊(D33×C101)
unambiguous semidirect productC11⋊(D15×C101)

Splittings

Fitting, socle, HallC3×C5×C11×C101 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C101
HallC5×C11×C101 ⋊ D3
HallC3×C11×C101 ⋊ D5
HallC3×C5×C101 ⋊ D11
HallC11×C101 ⋊ D15
HallC5×C101 ⋊ D33
HallC3×C101 ⋊ D55
HallC5×C11 ⋊ D3×C101
HallC3×C11 ⋊ D5×C101
HallC3×C5 ⋊ D11×C101
SylowC11 ⋊ D15×C101
SylowC5 ⋊ D33×C101
SylowC3 ⋊ C101×D55

Subgroups

subgroupG/H
center, hypercenterC101D165
commutator, cosocle, hypocenterC3×C5×C11C2×C101
FrattiniC1G
Fitting, socleC3×C5×C11×C101C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C101

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16665

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33330, 21);