Finite Group Databasebeta

C2×#20295903 #28378727

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20295903

Splittings

FittingC2×C22⋊C4×C109 ⋊ C4
SylowC109 ⋊ C2×#342

Subgroups

subgroupG/H
centerC22(C2×#89137)⋊C4
commutatorC22×C109C2×C42
FrattiniC23C22×#89137
FittingC2×C22⋊C4×C109C4
socleC22×C109#95
prime radicalC24×D109C22
cosocleC23×D109C23
hypercenterC2×C22⋊C4#89137
hypocenterC109C2×#342
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20205);