Finite Group Databasebeta

C2×D7×C22⋊C16 #13506459

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

Aliases

direct productC2×D7×C22⋊C16

Splittings

FittingC2×C7×C22⋊C16 ⋊ C2
SylowC7 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC22×C8C22×D7
commutatorC2×C7C23×C16
FrattiniC2×C8C23×D7
FittingC2×C7×C22⋊C16C2
socleC23×C7C22×C8
prime radicalC24×D7C8
cosocleC2×C7×C8C24
hypercenterC2×C22⋊C16D7
hypocenterC7C22×C22⋊C16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 322231);