Finite Group Databasebeta

C22×D397⋊C8 #38763593

order25408
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D397⋊C8
unambiguous semidirect productD397⋊(C22×C8)

Splittings

derived, SylowC397 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#13097544
commutator, hypocenterC397C23×C8
FrattiniC2C23×#13097544
FittingC22×C4×C397C4
socleC23×C397C2×C4
prime radicalC23×D397C4
cosocleDic397C24
LCSG ▷ C397
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

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, 1620);