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D4×(C2×D127)⋊C4 #30641547

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×(C2×D127)⋊C4

Splittings

FittingC2×C4×D4×C127 ⋊ C2
SylowC127 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D127
commutatorC22×C127C23×C4
FittingC2×C4×D4×C127C2
socle, cosocleC23×C127C24
prime radicalC22×D4×D127C2
hypercenterC2×C4×D4D127
hypocenterC127D4×C22⋊C4
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 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, 7327);