Finite Group Databasebeta

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D4×#14523232 #30647467

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#14523232

Splittings

SylowC127 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D127
commutator, socleC22×C127C23×C4
FittingC2×C4×D4×C127C2
prime radicalC22×D4×C127C4
cosocleC2×C4×C127C24
hypercenterC2×C4×D4D127
hypocenterC127D4×M16
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13247);