Finite Group Databasebeta

#472×D109 #28372735

order13952
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#472×D109

Splittings

Fitting#472×C109 ⋊ C2
SylowC109 ⋊ C2×#472

Subgroups

subgroupG/H
centerC2#121×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#472×C109C2
socleC2×C109C2×#121
hypercenter#472D109
hypocenterC109C2×#472
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 14213);