Finite Group Databasebeta

C2×#27211658 #41000776

order26816
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27211658

Splittings

SylowC419 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D419
commutatorC2×C419C22×C8
FrattiniC8C22×D419
FittingC22×C8×C419C2
socleC22×C419C2×C8
prime radicalC23×C419C8
cosocleC8×C419C23
hypercenterC22×C8D419
hypocenterC419C2×M32
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

6728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 964);