Finite Group Databasebeta

#449×D109 #28372229

order13952
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#449×D109

Splittings

Fitting#449×C109 ⋊ C2
SylowC109 ⋊ C2×#449

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#449×C109C2
socleC22×C109C22×D4
hypercenter#449D109
hypocenterC109C2×#449
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13707);