Finite Group Databasebeta

C2×C16×Dic14 #13507277

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×C16×Dic14

Splittings

SylowC7 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C16C2×D7
commutatorC2×C7C23×C16
FrattiniC2×C8C23×D7
FittingC2×C4×C7×C16C2
socle, prime radicalC23×C7C22×C8
cosocleC2×C7×C8C24
hypercenterC2×C4×C16D7
hypocenterC7C2×Q8×C16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1792

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 323049);