Finite Group Databasebeta

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H(3,ℤ/4)×Dic47 #26121441

order12032
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×Dic47

Splittings

SylowC47 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D47
commutatorC4×C47C43
FrattiniC23×C4C22×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47C2×#95
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47C4×H(3,ℤ/4)
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 74731);