Finite Group Databasebeta

C22×Dic1954 #44530706

order31264
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1954

Splittings

SylowC977 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D977
commutator, cosocleC2×C977C24
FrattiniC2C23×D977
FittingC22×C4×C977C2
socle, prime radicalC23×C977C22
hypercenterC22×C4D977
hypocenterC977C22×Q8
LCSG ▷ C2×C977 ▷ C977
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31264

Conjugacy classes & character table

7828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31264, 186);