Finite Group Databasebeta

C2×#27189658 #39909667

order26176
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27189658

Splittings

FittingC2×D8×C409 ⋊ C2
SylowC409 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22#20266973
commutator, cosocleC8×C409C23
FrattiniC8C22×D409
FittingC2×D8×C409C2
socleC22×C409D8
hypercenterC2×D8D409
hypocenterC409C2×D16
LCSG ▷ C8×C409 ▷ C4×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13088

Conjugacy classes & character table

2878 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 969);