Finite Group Databasebeta

C22×#20263719 #38763295

order25408
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#20263719

Splittings

SylowC397 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D397
commutator, cosocleC4×C397C24
FrattiniC4C23×D397
Fitting, prime radicalC22×D4×C397C2
socleC23×C397D4
hypercenterC22×D4D397
hypocenterC397C22×SD16
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

3988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1322);