Finite Group Databasebeta

C2×M16×#89137 #28379586

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×#89137

Splittings

FittingC2×M16×C109 ⋊ C4
SylowC109 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C22×C42
FrattiniC4C23×#89137
FittingC2×M16×C109C4
socleC22×C109C2×C42
prime radicalC23×D109C2×C4
cosocleC4×D109C24
hypercenterC2×M16#89137
hypocenterC109C2×C4×M16
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×M16

656 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, 21064);