Finite Group Databasebeta

D8×#6923 #16840798

order3904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×#6923

Splittings

FittingD8×C61 ⋊ C4
SylowC61 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2D4×#6923
commutatorC4×C61C22×C4
FrattiniC4C22×#6923
FittingD8×C61C4
socleC2×C61C4×D4
prime radicalD8×D61C2
cosocleC4×D61C23
hypercenterD8#6923
hypocenterC61C4×D8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C4 ◁ D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 488

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1585);