Finite Group Databasebeta

C2×#27211635 #41000338

order26816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27211635

Splittings

SylowC419 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic419
commutatorC22×C419C22×C4
FrattiniC2×C4C22×D419
Fitting, prime radicalC22×D4×C419C2
socleC22×C419C22⋊C4
cosocleC2×C4×C419C23
hypercenterC22×D4D419
hypocenterC419C2×#100
LCSG ▷ C22×C419 ▷ C2×C419 ▷ C419
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6704

Conjugacy classes & character table

4202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 526);