Finite Group Databasebeta

C22×Dic1838 #44440819

order29408
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1838

Splittings

SylowC919 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D919
commutator, cosocleC2×C919C24
FrattiniC2C23×D919
FittingC22×C4×C919C2
socle, prime radicalC23×C919C22
hypercenterC22×C4D919
hypocenterC919C22×Q8
LCSG ▷ C2×C919 ▷ C919
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29408

Conjugacy classes & character table

7364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29408, 186);