Finite Group Databasebeta

#344×D109 #28362772

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

Aliases

direct product#344×D109

Splittings

Fitting#344×C109 ⋊ C2
SylowC109 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D109
commutatorC22×C109C2×C42
FrattiniC22×C4C22×D109
Fitting#344×C109C2
socleC2×C109C2×#95
prime radicalC23×D109C2×C4
cosocleC22×C4×C109C23
hypercenter#344D109
hypocenterC109C2×#344
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

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, 4250);