Finite Group Databasebeta

C22×(C2×D7)⋊C16 #13506460

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D7)⋊C16

Splittings

FittingC23×C7×C16 ⋊ C2
SylowC7 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D7
commutatorC2×C7C23×C16
FrattiniC2×C8C23×D7
FittingC23×C7×C16C2
socleC24×C7C2×C8
prime radicalC24×D7C8
cosocleC2×C7×C8C24
hypercenterC23×C16D7
hypocenterC7C22×C22⋊C16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

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, 322232);