Finite Group Databasebeta

#121×#89137 #28379496

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

Aliases

direct product#121×#89137

Splittings

Fitting#121×C109 ⋊ C4
SylowC109 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
Fitting#121×C109C4
prime radical#121×D109C2
cosocleC22×D109C24
hypercenter#121#89137
hypocenterC109C4×#121
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ #121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20974);