Finite Group Databasebeta

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C22⋊C4×#4339 #14912975

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

Aliases

direct productC22⋊C4×#4339

Splittings

FittingC2×C4×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×#4339C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C22⋊C4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

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(2816, 328770);