Finite Group Databasebeta

C2×#41×Dic127 #30651912

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×Dic127

Splittings

SylowC127 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC2×C127C24×C4
FrattiniC22C24×D127
Fitting, prime radicalC22×#41×C127C2
socleC23×C127C24
cosocleC22×C127C25
hypercenterC22×#41D127
hypocenterC127C2×C4×#41
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C22×#41

1728 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17692);