Finite Group Databasebeta

C2×C4×(C2×D127)⋊C4 #30641061

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D127)⋊C4

Splittings

FittingC22×C42×C127 ⋊ C2
SylowC127 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D127
commutatorC2×C127C22×C42
FrattiniC23C23×D127
FittingC22×C42×C127C2
socleC24×C127C23
prime radicalC24×D127C22
cosocleC23×C127C24
hypercenterC22×C42D127
hypocenterC127C2×C4×C22⋊C4
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6841);