Finite Group Databasebeta

C23×C22⋊Dic109 #28376190

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊Dic109

Splittings

SylowC109 ⋊ C23×C22⋊C4

Subgroups

subgroupG/H
centerC25C2×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
Fitting, prime radicalC26×C109C2
socleC25×C109C22
cosocleC22×C109C25
hypercenterC26D109
hypocenterC109C23×C22⋊C4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C25 ◁ C26

4632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17668);