Finite Group Databasebeta

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C4×(C2×D47)⋊C16 #26131306

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×(C2×D47)⋊C16

Splittings

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

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC22×C8C22×D47
FittingC2×C4×C16×C47C2
socleC23×C47C22×C8
prime radicalC23×D47C2×C8
cosocleC22×C8×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C4×C22⋊C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

614 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84596);