Finite Group Databasebeta

D8×#13097544 #38763558

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×#13097544

Splittings

FittingD8×C397 ⋊ C4
SylowC397 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2D4×#13097544
commutatorC4×C397C22×C4
FrattiniC4C22×#13097544
FittingD8×C397C4
socleC2×C397C4×D4
prime radicalD8×D397C2
cosocleC4×D397C23
hypercenterD8#13097544
hypocenterC397C4×D8
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C4 ◁ D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1585);