Finite Group Databasebeta

← Prev (#27131962) Next (#27131964) →

C37×D165 #27131963

order12210
isoclinismisoclinic class of D165
automorphism?
homologyAbelianization (H1) = C2×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×D165
unambiguous semidirect productC3⋊(C37×D55)
unambiguous semidirect productC5⋊(C37×D33)
unambiguous semidirect productC11⋊(D15×C37)

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C37
HallC5×C11×C37 ⋊ D3
HallC3×C11×C37 ⋊ D5
HallC3×C5×C37 ⋊ D11
HallC11×C37 ⋊ D15
HallC5×C37 ⋊ D33
HallC3×C37 ⋊ D55
HallC5×C11 ⋊ D3×C37
HallC3×C11 ⋊ D5×C37
HallC3×C5 ⋊ D11×C37
SylowC11 ⋊ D15×C37
SylowC5 ⋊ C37×D33
SylowC3 ⋊ C37×D55

Subgroups

subgroupG/H
center, hypercenterC37D165
commutator, cosocle, hypocenterC3×C5×C11C2×C37
FrattiniC1G
Fitting, socleC3×C5×C11×C37C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3108 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD37×D165, D11×D15×C37, D407⋊D15, …
maximal normal subgroup ofD37×D165, D11×D15×C37, D407⋊D15, …
maximal quotient ofC37×Dic165, C2×C37×D165, C37×D495, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12210, 18);