Finite Group Databasebeta

C22×C4×#13097544 #38763582

order25408
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#13097544
unambiguous semidirect productD397⋊(C2×C42)

Splittings

FittingC22×C4×C397 ⋊ C4
derived, SylowC397 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#13097544
commutator, hypocenterC397C22×C42
FrattiniC2C23×#13097544
FittingC22×C4×C397C4
socleC23×C397C2×C4
prime radicalC23×D397C22
cosocleC2×D397C24
LCSG ▷ C397
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

1648 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1609);