Finite Group Databasebeta

#416×D127 #30647222

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#416×D127

Splittings

Fitting#416×C127 ⋊ C2
SylowC127 ⋊ C2×#416

Subgroups

subgroupG/H
centerC2×C4D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
Fitting#416×C127C2
socleC22×C127C22×D4
prime radicalC2×#41×D127C2
cosocleC2×C4×C127C24
hypercenter#416D127
hypocenterC127C2×#416
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

792 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, 13002);