Finite Group Databasebeta

C2×#41×#89137 #28380008

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

Aliases

direct productC2×#41×#89137
unambiguous semidirect productD109⋊(C4×#41)

Splittings

FittingC2×#41×C109 ⋊ C4
SylowC109 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C24×C4
FrattiniC2C24×#89137
FittingC2×#41×C109C4
socleC22×C109C23×C4
prime radicalC2×#41×D109C2
cosocleC2×D109C25
hypercenterC2×#41#89137
hypocenterC109C2×C4×#41
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×#41

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21486);