Finite Group Databasebeta

← Prev (#49115010) Next (#49115012) →

C2×C32×C7×D143 #49115011

order36036
automorphism?
homologyAbelianization (H1) = C22×C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C7×D143
unambiguous semidirect product(C2×C11)⋊(C32×C7×D13)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC11×C13 ⋊ C22×C32×C7
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C22×C32
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC32×C13 ⋊ C2×C7×D11
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C32×D11
HallC7×C11 ⋊ C2×C32×D13
SylowC13 ⋊ C2×C32×C7×D11
SylowC11 ⋊ C2×C32×C7×D13

Subgroups

subgroupG/H
center, hypercenterC2×C32×C7D143
commutator, cosocle, hypocenterC11×C13C22×C32×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C11×C13
UCSC1 ◁ C2×C32×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 679);