Finite Group Databasebeta

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C2×C4⋊(C47⋊C32) #26136758

order12032
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊(C47⋊C32)

Splittings

SylowC47 ⋊ C2×C4⋊C32

Subgroups

subgroupG/H
centerC22×C16C2×D47
commutatorC2×C47C22×C32
FrattiniC2×C16C22×D47
FittingC2×C4×C16×C47C2
socle, prime radicalC23×C47C2×C16
cosocleC2×C16×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C2×C4⋊C32
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

230 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, 90048);