Finite Group Databasebeta

C2×#20295914 #28379232

order13952
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20295914

Splittings

SylowC109 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C4C2×#89137
commutatorC2×C109C2×C4×C8
FrattiniC2×C4C22×#89137
FittingC2×C42×C109C4
socle, prime radicalC23×C109C2×C8
cosocleC2×#11724784C23
hypercenterC2×C42#89137
hypocenterC109C2×#346
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C42

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20710);