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M16×(C2×D47)⋊C4 #26213911

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productM16×(C2×D47)⋊C4

Splittings

FittingC2×C4×M16×C47 ⋊ C2
SylowC47 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×M16×C47C2
socleC23×C47C23×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C22⋊C4×M16
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

1774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167201);