Finite Group Databasebeta

C4×#16861242 #30647553

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

Aliases

direct productC4×#16861242

Splittings

FittingC4×M16×C127 ⋊ C2
SylowC127 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2×C4C2×D508
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC4×M16×C127C2
socleC22×C127C22×D4
prime radicalC2×#14523248C22
cosocleC2×C4×C127C24
hypercenterC4×M16D127
hypocenterC127C4×#137
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

484 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13333);