Finite Group Databasebeta

#137×Dic109 #28371853

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×Dic109

Splittings

SylowC109 ⋊ C4×#137

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC2×#137×C109C2
socleC22×C109C22×D4
prime radicalC2×#41×C109C22
cosocleC2×C4×C109C24
hypercenterC2×#137D109
hypocenterC109C4×#137
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13331);