Finite Group Databasebeta

#529×D109 #28376290

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#529×D109

Splittings

Fitting#529×C109 ⋊ C2
SylowC109 ⋊ C2×#529

Subgroups

subgroupG/H
centerC2×C4C23×D109
commutator, socle, cosocleC22×C109C25
FrattiniC22C24×D109
Fitting#529×C109C2
prime radical#121×D109C2
hypercenter#529D109
hypocenterC109C2×#529
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ #529

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17768);