Finite Group Databasebeta

C2×#20294980 #28371443

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

Aliases

direct productC2×#20294980

Splittings

FittingC2×C4×C8×C109 ⋊ C2
SylowC109 ⋊ C2×#405

Subgroups

subgroupG/H
centerC22×C8C2×D109
commutatorC2×C109C22×C42
FrattiniC2×C4C23×D109
FittingC2×C4×C8×C109C2
socleC23×C109C22×C4
prime radicalC23×D109C2×C4
cosocleC2×C4×C109C24
hypercenterC2×C4×C8D109
hypocenterC109C2×#405
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12921);