Finite Group Databasebeta

C22×#20263318 #38755965

order25216
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#20263318

Splittings

SylowC197 ⋊ C22×#125

Subgroups

subgroupG/H
centerC24C22×D197
commutator, cosocleC22×C197C25
FrattiniC22C24×D197
FittingC22×C42×C197C2
socle, prime radicalC24×C197C23
hypercenterC22×C42D197
hypocenterC197C22×#125
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C24 ◁ C22×C42

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

6328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 17763);