Finite Group Databasebeta

C2×D109⋊C32 #28379451

order13952
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C23

Aliases

direct productC2×D109⋊C32
unambiguous semidirect productD109⋊(C2×C32)

Splittings

derived, SylowC109 ⋊ C22×C32

Subgroups

subgroupG/H
center, hypercenterC2×C16#89137
commutator, hypocenterC109C22×C32
FrattiniC8C22×#89137
FittingC2×C16×C109C4
socleC22×C109C2×C16
prime radicalC22×D109C16
cosocle#13182004C23
LCSG ▷ C109
UCSC1 ◁ C2×C16

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20929);