Finite Group Databasebeta

C2×#20294954 #28366259

order13952
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20294954

Splittings

SylowC109 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D109
commutator, cosocleC23×C109C24
FrattiniC23C23×D109
FittingC22×C22⋊C4×C109C2
socleC24×C109C23
prime radicalC25×C109C22
hypercenterC22×C22⋊C4D109
hypocenterC109C2×#397
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7737);