Finite Group Databasebeta

C2×#20296093 #28380009

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20296093
unambiguous semidirect productD109⋊#518

Splittings

FittingC22×D4×C109 ⋊ C4
SylowC109 ⋊ C2×#518

Subgroups

subgroupG/H
centerC22C23×#89137
commutatorC2×C109C24×C4
FrattiniC2C24×#89137
FittingC22×D4×C109C4
socleC22×C109C23×C4
prime radicalC22×D4×D109C2
cosocleC2×D109C25
hypercenterC22×D4#89137
hypocenterC109C2×#518
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×D4

1920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21487);