Finite Group Databasebeta

C2×D397⋊C16 #38763576

order25408
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×D397⋊C16
unambiguous semidirect productD397⋊(C2×C16)

Splittings

derived, SylowC397 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC2×C8#13097544
commutator, hypocenterC397C22×C16
FrattiniC4C22×#13097544
FittingC2×C8×C397C4
socleC22×C397C2×C8
prime radicalC22×D397C8
cosocle#15691787C23
LCSG ▷ C397
UCSC1 ◁ C2×C8

98 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, 1603);