Finite Group Databasebeta

D4×#15691794 #38763548

order25408
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#15691794

Splittings

SylowC397 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#13097544
commutatorC2×C397C22×C8
Fitting, prime radicalC2×D4×C397C4
socleC22×C397C22×C4
cosocleC2×Dic397C23
hypercenterC2×D4#13097544
hypocenterC397C8×D4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

1030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1575);