Finite Group Databasebeta

C23×C4⋊Dic109 #28376193

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×C4⋊Dic109

Splittings

SylowC109 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC25C2×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC24×C4×C109C2
socle, prime radicalC25×C109C22
cosocleC22×C109C25
hypercenterC24×C4D109
hypocenterC109C23×C4⋊C4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C25 ◁ C24×C4

2488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

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, 17671);