Finite Group Databasebeta

C2×M16×D28 #14217699

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×M16×D28

Splittings

FittingC2×C4×C7×M16 ⋊ C2
SylowC7 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C4×C7×M16C2
socleC23×C7C23×C4
prime radicalC23×D28C4
cosocleC2×C4×C7C25
hypercenterC2×C4×M16D7
hypocenterC7C2×D4×M16
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1033471);