Finite Group Databasebeta

← Prev (#22579608) Next (#22579610) →

C22×(C67⋊C3)⋊C11 #22579609

order8844
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×(C67⋊C3)⋊C11
unambiguous semidirect product(C22×C67⋊C3)⋊C11

Splittings

Fitting, socle, HallC22×C67 ⋊ C3×C11
derived, SylowC67 ⋊ C22×C3×C11
HallC22×C67⋊C11 ⋊ C3
HallC22×C67⋊C3 ⋊ C11
HallC67⋊C11 ⋊ C22×C3
HallC67⋊C3 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC22(C67⋊C3)⋊C11
commutator, hypocenterC67C22×C3×C11
FrattiniC1G
Fitting, socleC22×C67C3×C11
LCSG ▷ C67
UCSC1 ◁ C22

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×(C67⋊C3)⋊C11, C2×D3×(C67⋊C3)⋊C11, C22×C3×(C67⋊C3)⋊C11
maximal normal subgroup ofA4×(C67⋊C3)⋊C11, C22×C3×(C67⋊C3)⋊C11
maximal quotient ofC22×(C67⋊C9)⋊C11, C2×D3×(C67⋊C3)⋊C11, C22×C3×(C67⋊C3)⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8844, 22);