Finite Group Databasebeta

← Prev (#10620349) Next (#10620351) →

C22×C3×C11⋊C5 #10620350

order660
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C11⋊C5
unambiguous semidirect product(C22×C3×C11)⋊C5

Splittings

Fitting, socle, HallC22×C3×C11 ⋊ C5
derived, SylowC11 ⋊ C22×C3×C5
HallC22×C11 ⋊ C3×C5
HallC3×C11 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3C11⋊C5
commutator, cosocle, hypocenterC11C22×C3×C5
FrattiniC1G
Fitting, socleC22×C3×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2)(5,6,7)(9,10,12,15,14)(11,13,17,18,16);(3,4)(8,9,11,14,10,12,16,18,13,15,17)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×Dic11⋊C5, C3×C22⋊AGL(1,𝔽11), C2×Dic3×C11⋊C5, …
maximal normal subgroup ofC2×C3×Dic11⋊C5, C3×C22⋊AGL(1,𝔽11), C2×Dic3×C11⋊C5, …
maximal quotient ofC2×C3×C4×C11⋊C5, C3×D4×C11⋊C5, C3×Q8×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 20);