Finite Group Databasebeta

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C2×C4×C16×D47 #26368899

order12032
isoclinismisoclinic class of D47
automorphism?
homologyAbelianization (H1) = C22×C4×C16 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C16×D47

Splittings

FittingC2×C4×C16×C47 ⋊ C2
derived, SylowC47 ⋊ C22×C4×C16

Subgroups

subgroupG/H
center, hypercenterC2×C4×C16D47
commutator, hypocenterC47C22×C4×C16
FrattiniC2×C8C23×D47
FittingC2×C4×C16×C47C2
socleC23×C47C22×C8
prime radicalC23×D47C2×C8
cosocleC2×C8×C47C24
LCSG ▷ C47
UCSC1 ◁ C2×C4×C16

1022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322189);