Finite Group Databasebeta

#137×#90673 #28407330

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×#90673

Splittings

Fitting#137×C113 ⋊ C4
SylowC113 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2C2×D4×#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
Fitting#137×C113C4
socleC2×C113C2×C4×D4
prime radical#41×D113C22
cosocleC4×D113C24
hypercenter#137#90673
hypocenterC113C4×#137
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21266);