Finite Group Databasebeta

D4×#90781 #16822309

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#90781

Splittings

FittingC2×C4×D4×C29 ⋊ C2
SylowC29 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC2×C4×D4×C29C2
socle, cosocleC23×C29C24
prime radicalC22×D4×D29C2
hypercenterC2×C4×D4D29
hypocenterC29D4×C22⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 7327);