Finite Group Databasebeta

← Prev (#49115006) Next (#49115008) →

C22×C3×C11×#63270 #49115007

order36036
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C11×#63270

Splittings

Fitting, socleC22×C3×C7×C11×C13 ⋊ C3
derived, HallC7×C13 ⋊ C22×C32×C11
HallC22×C7×C11×C13 ⋊ C32
HallC7×C11×C13 ⋊ C22×C32
HallC22×C11×C13 ⋊ C3×ΓL(1,𝔽8)
HallC22×C7×C13 ⋊ C32×C11
HallC22×C7×C11 ⋊ C3×C13⋊C3
HallC11×C13 ⋊ C22×C3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C22×C3×C13⋊C3
HallC22×C13 ⋊ C3×C11×ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C11×C13⋊C3
SylowC13 ⋊ C22×C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C3×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C3×C11#63270
commutator, cosocle, hypocenterC7×C13C22×C32×C11
FrattiniC1G
Fitting, socleC22×C3×C7×C11×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C3×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12012

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 675);