Finite Group Databasebeta

← Prev (#31825081) Next (#31825083) →

C7×C13×C3⋊D33 #31825082

order18018
isoclinismisoclinic class of C3⋊D33
automorphism?
homologyAbelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C3

Aliases

direct productC7×C13×C3⋊D33
unambiguous semidirect productC3⋊(C7×C13×D33)
unambiguous semidirect productC11⋊(C7×C13×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derived, HallC32×C11 ⋊ C2×C7×C13
HallC32×C11×C13 ⋊ C2×C7
HallC7×C11×C13 ⋊ C3⋊D3
HallC32×C7×C13 ⋊ D11
HallC32×C7×C11 ⋊ C2×C13
HallC11×C13 ⋊ C7×C3⋊D3
HallC32×C13 ⋊ C7×D11
HallC7×C11 ⋊ C13×C3⋊D3
HallC32×C7 ⋊ C13×D11
SylowC11 ⋊ C7×C13×C3⋊D3
SylowC32 ⋊ C7×C13×D11

Subgroups

subgroupG/H
center, hypercenterC7×C13C3⋊D33
commutator, cosocle, hypocenterC32×C11C2×C7×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C32×C11
UCSC1 ◁ C7×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

4641 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C13×D33, C7×D39⋊D33, C13×D21⋊D33, …
maximal normal subgroup ofD3×C7×C13×D33, C7×D39⋊D33, C13×D21⋊D33, …
maximal quotient ofC7×C13×C3⋊Dic33, C2×C7×C13×C3⋊D33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 127);