Finite Group Databasebeta

C2×#125×D109 #28376282

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

Aliases

direct productC2×#125×D109

Splittings

FittingC2×#125×C109 ⋊ C2
SylowC109 ⋊ C22×#125

Subgroups

subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×#125×C109C2
socleC23×C109C24
prime radicalC23×D109C23
hypercenterC2×#125D109
hypocenterC109C22×#125
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#125

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17760);