Finite Group Databasebeta

C23×C22⋊#1055 #16726346

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊#1055

Splittings

SylowC13 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC25×C4×C13C2
socleC25×C13C2×C4
prime radicalC26×C13C4
cosocleC2×C4×C13C25
hypercenterC25×C4D13
hypocenterC13C23×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 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, 1032995);