Finite Group Databasebeta

D4×C22⋊Dic31 #16848533

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊Dic31

Splittings

SylowC31 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
Fitting, prime radicalC23×D4×C31C2
socle, cosocleC23×C31C24
hypercenterC23×D4D31
hypocenterC31D4×C22⋊C4
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 7332);