Finite Group Databasebeta

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D4×C4⋊C4×D47 #26375558

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×C4⋊C4×D47

Splittings

FittingD4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingD4×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenterD4×C4⋊C4D47
hypocenterC47C2×D4×C4⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ D4×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328848);