Finite Group Databasebeta

C22⋊C4×D983 #44537913

order31456
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D983

Splittings

FittingC22⋊C4×C983 ⋊ C2
SylowC983 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D983
commutatorC2×C983C22×C4
FittingC22⋊C4×C983C2
socle, cosocleC22×C983C23
prime radicalC23×D983C2
hypercenterC22⋊C4D983
hypocenterC983C2×C22⋊C4
LCSG ▷ C2×C983 ▷ C983
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7864

Conjugacy classes & character table

4930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 96);