Finite Group Databasebeta

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C22×C5×D44 #13183412

order1760
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC22×C5×D44

Splittings

FittingC22×C4×C5×C11 ⋊ C2
HallC5×C11 ⋊ C22×D4
SylowC11 ⋊ C22×C5×D4

Subgroups

subgroupG/H
centerC23×C5C2×D11
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×C5×D11
FittingC22×C4×C5×C11C2
socleC23×C5×C11C22
hypercenterC22×C4×C5D11
hypocenterC11C22×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1221);