Finite Group Databasebeta

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C16×C22⋊Dic47 #26131357

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

Aliases

direct productC16×C22⋊Dic47

Splittings

SylowC47 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
centerC22×C16C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC22×C8C22×D47
FittingC23×C16×C47C2
socleC23×C47C22×C8
prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC23×C16D47
hypocenterC47C16×C22⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C16 ◁ C23×C16

510 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, 84647);