Finite Group Databasebeta

C2×C22⋊#16809897 #41003807

order26944
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#16809897

Splittings

SylowC421 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#13132997
commutatorC2×C421C22×C8
FrattiniC22C22×#13132997
Fitting, prime radicalC24×C421C4
socleC23×C421C2×C4
cosocleC2×Dic421C23
hypercenterC24#13132997
hypocenterC421C2×C22⋊C8
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C23 ◁ C24

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1516);