Finite Group Databasebeta

C23×#88055 #16726301

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88055

Splittings

SylowC13 ⋊ C23×#97

Subgroups

subgroupG/H
centerC24×C4C2×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC24×C8×C13C2
socle, prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC24×C8D13
hypocenterC13C23×#97
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24×C4 ◁ C24×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 1032950);