Finite Group Databasebeta

C2×#20295560 #28376298

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20295560

Splittings

FittingC22×C42×C109 ⋊ C2
SylowC109 ⋊ C2×#529

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC22×C42×C109C2
socleC23×C109C24
prime radicalC2×#16812673C2
hypercenterC22×C42D109
hypocenterC109C2×#529
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C22×C42

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17776);