Finite Group Databasebeta

C23×#88126 #16769477

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#88126

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC23×C42×C13C2
socleC25×C13C23
prime radicalC25×D13C22
cosocleC22×C13C26
hypercenterC23×C42D13
hypocenterC13C23×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076126);