Finite Group Databasebeta

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C4×#10622137 #14673950

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#10622137

Splittings

SylowC11 ⋊ C4×M64

Subgroups

subgroupG/H
centerC4×C16C2×D11
commutatorC2×C11C2×C4×C16
FrattiniC2×C16C22×D11
FittingC2×C4×C11×C16C2
socleC22×C11C22×C16
prime radicalC23×C11C2×C16
cosocleC2×C11×C16C23
hypercenterC2×C4×C16D11
hypocenterC11C4×M64
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 89745);