Finite Group Databasebeta

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C22×#10622448 #15617484

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#10622448

Splittings

FittingC22×C11×C4⋊C8 ⋊ C2
SylowC11 ⋊ C22×#432

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊C8C2
socleC24×C11C22×C4
prime radicalC24×D11C2×C4
cosocleC2×C4×C11C25
hypercenterC22×C4⋊C8D11
hypocenterC11C22×#432
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033279);