Finite Group Databasebeta

C22×#20263718 #38763294

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

Aliases

direct productC22×#20263718

Splittings

FittingC22×Q8×C397 ⋊ C2
SylowC397 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D397
commutator, cosocleC4×C397C24
FrattiniC4C23×D397
FittingC22×Q8×C397C2
socleC23×C397D4
prime radicalC22×D1588C2
hypercenterC22×Q8D397
hypocenterC397C22×SD16
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

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, 1321);