Finite Group Databasebeta

Q8×#14523247 #30652307

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#14523247

Splittings

FittingD4×Q8×C127 ⋊ C2
SylowC127 ⋊ Q8×#41

Subgroups

subgroupG/H
center, FrattiniC22C24×D127
commutator, socle, cosocleC22×C127C25
FittingD4×Q8×C127C2
prime radicalC2×#14523247C22
hypercenterD4×Q8D127
hypocenterC127Q8×#41
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ D4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 18087);