Finite Group Databasebeta

D4×C22⋊Dic281 #49098125

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊Dic281

Splittings

SylowC281 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
Fitting, prime radicalC23×D4×C281C2
socle, cosocleC23×C281C24
hypercenterC23×D4D281
hypocenterC281D4×C22⋊C4
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C23×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

5650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 7332);