Finite Group Databasebeta

C23×#88180 #16769479

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

Aliases

direct productC23×#88180

Splittings

SylowC13 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC25×C4×C13C2
socleC25×C13C23
prime radicalC26×C13C22
cosocleC22×C13C26
hypercenterC25×C4D13
hypocenterC13C23×#117
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24×C4 ◁ C25×C4

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, 1076128);