Finite Group Databasebeta

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D4×(C22⋊D11)⋊C4 #14913555

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×(C22⋊D11)⋊C4

Splittings

FittingD4×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ C4×D42

Subgroups

subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC2×D4×C22⋊D11C2
hypercenterD4×C22⋊C4D11
hypocenterC11C4×D42
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

4804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 329350);