Finite Group Databasebeta

#123×Dic127 #30641253

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

Aliases

direct product#123×Dic127

Splittings

SylowC127 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D127
commutatorC22×C127C23×C4
FittingC2×#123×C127C2
socle, cosocleC23×C127C24
prime radicalC22×D4×C127C22
hypercenterC2×#123D127
hypocenterC127C4×#123
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×#123

688 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 7033);