Finite Group Databasebeta

C4×#16861192 #30641252

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

Aliases

direct productC4×#16861192

Splittings

FittingC22×C42×C127 ⋊ C2
SylowC127 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC22×C42×C127C2
socle, cosocleC23×C127C24
prime radicalC22×C22⋊D127C22
hypercenterC22×C42D127
hypocenterC127C4×#123
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C22×C42

688 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 7032);