Finite Group Databasebeta

C2×#27163035 #38762936

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

Aliases

direct productC2×#27163035

Splittings

FittingC2×C16×C397 ⋊ C2
SylowC397 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D397
commutatorC2×C397C22×C8
FrattiniC8C22×D397
FittingC2×C16×C397C2
socleC22×C397C2×C8
prime radicalC22×D397C8
cosocleC8×C397C23
hypercenterC2×C16D397
hypocenterC397C2×M32
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

6376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 963);