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C4×#10623304 #15617853

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

Aliases

direct productC4×#10623304

Splittings

FittingC4×C11×AGL(1,ℤ/8) ⋊ C2
SylowC11 ⋊ C4×#575

Subgroups

subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC4×C11×AGL(1,ℤ/8)C2
socleC22×C11C23×D4
prime radicalC2×#10623304C2
cosocleC2×C4×C11C25
hypercenterC4×AGL(1,ℤ/8)D11
hypocenterC11C4×#575
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

2842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033648);