Finite Group Databasebeta

C22⋊C4×C22⋊D31 #16848530

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

Aliases

direct productC22⋊C4×C22⋊D31

Splittings

FittingC22×C22⋊C4×C31 ⋊ C2
SylowC31 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC22×C22⋊C4×C31C2
socle, cosocleC23×C31C24
prime radicalC23×C22⋊D31C2
hypercenterC22×C22⋊C4D31
hypocenterC31D4×C22⋊C4
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C22⋊C4

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, 7329);