Finite Group Databasebeta

← Prev (#20294198) Next (#20294200) →

C3×C7×D165 #20294199

order6930
isoclinismisoclinic class of D165
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D165
unambiguous semidirect productC3⋊(C3×C7×D55)
unambiguous semidirect productC5⋊(C3×C7×D33)
unambiguous semidirect productC11⋊(C3×C7×D15)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derivedC3×C5×C11 ⋊ C2×C3×C7
HallC32×C7×C11 ⋊ D5
HallC32×C5×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ C3×D3
HallC32×C5×C7 ⋊ D11
HallC32×C11 ⋊ C7×D5
HallC7×C11 ⋊ C3×D15
HallC32×C7 ⋊ D55
HallC5×C11 ⋊ C3×D3×C7
HallC32×C5 ⋊ C7×D11
HallC5×C7 ⋊ C3×D33
SylowC11 ⋊ C3×C7×D15
SylowC32 ⋊ C7×D55
SylowC5 ⋊ C3×C7×D33

Subgroups

subgroupG/H
center, hypercenterC3×C7D165
commutator, hypocenterC3×C5×C11C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D11×D15, C3×D7×D165, C3×D77⋊D15, …
maximal normal subgroup ofC3×C7×D11×D15, C3×D7×D165, C3×D77⋊D15, …
maximal quotient ofC3×C7×Dic165, C2×C3×C7×D165, C3×C7×D825, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 86);