Finite Group Databasebeta

#137×#89137 #28379788

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

Aliases

direct product#137×#89137

Splittings

Fitting#137×C109 ⋊ C4
SylowC109 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2C2×D4×#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
Fitting#137×C109C4
socleC2×C109C2×C4×D4
prime radical#41×D109C22
cosocleC4×D109C24
hypercenter#137#89137
hypocenterC109C4×#137
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21266);