Finite Group Databasebeta

← Prev (#49115014) Next (#49115016) →

C2×C32×D1001 #49115015

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

Aliases

direct productC2×C32×D1001
unambiguous semidirect product(C2×C11)⋊(C32×D91)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC7×C11×C13 ⋊ C22×C32
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D7
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C32×D7
HallC32×C13 ⋊ C2×D77
HallC32×C11 ⋊ C2×D91
HallC7×C13 ⋊ C2×C32×D11
HallC7×C11 ⋊ C2×C32×D13
HallC32×C7 ⋊ C2×D143
SylowC13 ⋊ C2×C32×D77
SylowC11 ⋊ C2×C32×D91
SylowC7 ⋊ C2×C32×D143

Subgroups

subgroupG/H
center, hypercenterC2×C32D1001
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C32

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 683);