Finite Group Databasebeta

D4×C4⋊Dic31 #16848613

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×C4⋊Dic31

Splittings

SylowC31 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C4×D4×C31C2
socle, cosocleC23×C31C24
prime radicalC22×D4×C31C22
hypercenterC2×C4×D4D31
hypocenterC31D4×C4⋊C4
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 7412);