Finite Group Databasebeta

#413×D109 #28371503

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#413×D109

Splittings

Fitting#413×C109 ⋊ C2
SylowC109 ⋊ C2×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×D109
commutatorC22×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#413×C109C2
socleC2×C109C22×C22⋊C4
prime radicalC2×#41×D109C2
cosocleC2×C4×C109C24
hypercenter#413D109
hypocenterC109C2×#413
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

756 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, 12981);