Finite Group Databasebeta

C2×#20294926 #28365486

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#20294926

Splittings

FittingC22×C22⋊C4×C109 ⋊ C2
SylowC109 ⋊ C2×#390

Subgroups

subgroupG/H
centerC24C22×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
FittingC22×C22⋊C4×C109C2
socleC24×C109C23
prime radicalC23×C22⋊D109C2
cosocleC23×C109C24
hypercenterC22×C22⋊C4D109
hypocenterC109C2×#390
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6964);