Finite Group Databasebeta

#123×#89137 #28379497

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

Aliases

direct product#123×#89137

Splittings

Fitting#123×C109 ⋊ C4
SylowC109 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
Fitting#123×C109C4
prime radicalC2×D4×D109C22
cosocleC22×D109C24
hypercenter#123#89137
hypocenterC109C4×#123
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ #123

688 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, 20975);