Finite Group Databasebeta

C2×#27163037 #38762942

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

Aliases

direct productC2×#27163037

Splittings

FittingC2×D8×C397 ⋊ C2
SylowC397 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22#20263716
commutator, cosocleC8×C397C23
FrattiniC8C22×D397
FittingC2×D8×C397C2
socleC22×C397D8
hypercenterC2×D8D397
hypocenterC397C2×D16
LCSG ▷ C8×C397 ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

2794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 969);