Finite Group Databasebeta

C2×#27211725 #41001124

order26816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27211725

Splittings

SylowC419 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D419
commutatorC2×C419C23×C4
FrattiniC4C23×D419
Fitting, prime radicalC2×#41×C419C2
socleC22×C419C22×C4
cosocleC4×C419C24
hypercenterC2×#41D419
hypocenterC419C2×#131
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

4220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 1312);