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C4×#10622814 #14759665

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#10622814

Splittings

FittingC4×C11×AGL(1,ℤ/8) ⋊ C2
SylowC11 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C2×#120
prime radicalC2×#10622814C2
cosocleC22×C4×C11C24
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11C4×#454
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 175460);