Finite Group Databasebeta

C2×Q16×D263 #30682713

order16832
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q16×D263

Splittings

FittingC2×Q16×C263 ⋊ C2
SylowC263 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC22D4×D263
commutator, cosocleC4×C263C24
FrattiniC4C23×D263
FittingC2×Q16×C263C2
socleC22×C263C2×D4
prime radicalC22×D263D4
hypercenterC2×Q16D263
hypocenterC263C22×Q16
LCSG ▷ C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

1862 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 1324);