Finite Group Databasebeta

D4×#15691787 #38762588

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

Aliases

direct productD4×#15691787

Splittings

SylowC397 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D397
commutatorC2×C397C22×C8
FittingC4×D4×C397C2
socleC22×C397C22×C4
prime radicalC2×D4×C397C4
cosocleC2×C4×C397C23
hypercenterC4×D4D397
hypocenterC397C8×D4
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ C4×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 615);