Finite Group Databasebeta

#339×D109 #28362736

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D109

Splittings

Fitting#339×C109 ⋊ C2
SylowC109 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D109
commutatorC4×C109C2×C42
FrattiniC22×C4C22×D109
Fitting#339×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC23×D109D4
cosocleC22×C4×C109C23
hypercenter#339D109
hypocenterC109C2×#339
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

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, 4214);