Finite Group Databasebeta

← Prev (#19104243) Next (#19104245) →

C2×C13×C3⋊D33 #19104244

order5148
isoclinismisoclinic class of C3⋊D33
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C13×C3⋊D33
unambiguous semidirect product(C2×C3)⋊(C13×D33)
unambiguous semidirect product(C2×C11)⋊(C13×C3⋊D3)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derived, HallC32×C11 ⋊ C22×C13
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C2×C3⋊D3
HallC32×C13 ⋊ C2×D11
SylowC11 ⋊ C2×C13×C3⋊D3
SylowC32 ⋊ C2×C13×D11

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊D33
commutator, hypocenterC32×C11C22×C13
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C32×C11
UCSC1 ◁ C2×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×C3⋊(C3⋊AGL(1,𝔽11)), D5×C13×C3⋊D33, C2×C5×C13×C3⋊D33, …
maximal normal subgroup ofC2×C13×C3⋊(C3⋊AGL(1,𝔽11)), C2×C5×C13×C3⋊D33, C2×C7×C13×C3⋊D33
maximal quotient ofD5×C13×C3⋊D33, C2×C5×C13×C3⋊D33, C2×C13×C3⋊D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 120);