Finite Group Databasebeta

← Prev (#13089527) Next (#13089529) →

C22×A6 #13089528

order1440
isoclinismisoclinic class of A6
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C22×C3

Aliases

direct productC22×A6

Subgroups

subgroupG/H
center, Fitting, hypercenterC22A6
commutator, hypocenterA6C22
FrattiniC1G
LCSG ▷ A6
UCSC1 ◁ C22

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

socle ofS4×A6, C2×C4×A6, C22×S6
maximal subgroup ofA4×A6, D4×A6, C2×C4×A6, …
maximal normal subgroup ofA4×A6, D4×A6, C2×C4×A6, …
maximal quotient ofD4×A6, C22×SL(2,𝔽9), Q8×A6, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5845);