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C2×C7×D423 #26044885

order11844
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D423
unambiguous semidirect product(C2×C9)⋊(C7×D47)
unambiguous semidirect product(C2×C47)⋊(C7×D9)

Splittings

FittingC2×C7×C9×C47 ⋊ C2
derived, HallC9×C47 ⋊ C22×C7
HallC7×C9×C47 ⋊ C22
HallC7×C47 ⋊ C2×D9
HallC7×C9 ⋊ C2×D47
SylowC47 ⋊ C2×C7×D9
SylowC9 ⋊ C2×C7×D47

Subgroups

subgroupG/H
center, hypercenterC2×C7D423
commutator, cosocle, hypocenterC9×C47C22×C7
FrattiniC3C2×C7×D141
FittingC2×C7×C9×C47C2
socleC2×C3×C7×C47D3
LCSG ▷ C9×C47
UCSC1 ◁ C2×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 32);