Finite Group Databasebeta

D4×#16860614 #44542381

order31904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×#16860614

Splittings

FittingD4×C997 ⋊ C4
SylowC997 ⋊ C4×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×#16860614
commutator, socleC2×C997C22×C4
FittingD4×C997C4
prime radicalD4×D997C2
cosocleC2×D997C23
hypercenterD4#16860614
hypocenterC997C4×D4
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C2 ◁ D4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3988

Conjugacy classes & character table

1265 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31904, 226);