Finite Group Databasebeta

#520×D109 #28376224

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#520×D109

Splittings

Fitting#520×C109 ⋊ C2
SylowC109 ⋊ C2×#520

Subgroups

subgroupG/H
center, FrattiniC22C24×D109
commutatorC2×C109C24×C4
Fitting#520×C109C2
socle, cosocleC22×C109C25
prime radicalC2×#41×D109C2
hypercenter#520D109
hypocenterC109C2×#520
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #520

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17702);