Finite Group Databasebeta

C22×Dic1966 #44538003

order31456
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1966

Splittings

SylowC983 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D983
commutator, cosocleC2×C983C24
FrattiniC2C23×D983
FittingC22×C4×C983C2
socle, prime radicalC23×C983C22
hypercenterC22×C4D983
hypocenterC983C22×Q8
LCSG ▷ C2×C983 ▷ C983
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31456

Conjugacy classes & character table

7876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 186);