Finite Group Databasebeta

← Prev (#19104241) Next (#19104243) →

C22×C3×C11×C13⋊C3 #19104242

order5148
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C11×C13⋊C3

Splittings

Fitting, socleC22×C3×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C32×C11
HallC22×C11×C13 ⋊ C32
HallC11×C13 ⋊ C22×C32
HallC22×C13 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC22×C3×C11C13⋊C3
commutator, hypocenterC13C22×C32×C11
FrattiniC1G
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C3×C13⋊C3×C11⋊C5, C2×C3×D5×C11×C13⋊C3, C22×C3×C5×C11×C13⋊C3, …
maximal normal subgroup ofC22×C3×C13⋊C3×C11⋊C5, C22×C3×C5×C11×C13⋊C3, C22×C3×C7×C11×C13⋊C3
maximal quotient ofC2×C3×D5×C11×C13⋊C3, C22×C3×C5×C11×C13⋊C3, C2×C11×C13⋊C3×AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 118);