Finite Group Databasebeta

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C4×#15688908 #26131329

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688908

Splittings

FittingC4×M32×C47 ⋊ C2
SylowC47 ⋊ C4×#350

Subgroups

subgroupG/H
centerC4×C8C22⋊D47
commutatorC4×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC4×M32×C47C2
socleC22×C47C2×C22⋊C8
prime radicalC2×#10625350C2×C4
cosocleC22×C8×C47C23
hypercenterC4×M32D47
hypocenterC47C4×#350
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C4×M32

490 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84619);